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The game's native resolution is 640x480, thrice that is 1920x1440, not 1920x1080. Not sure what exactly they ended up with, but I assume a non-integer scaling factor and black bars on the sides.

Anyway, you should never prevent people from changing the display settings.

Picking a higher resolution means the game is upscaled in its entirety. Why would you want to disable that?

(Unless your AGS version is really really old and you aren't talking about x2 / x3 / x4 filters but switching the actual resolution, in which case you should upgrade your game to a more recent version of AGS.)

The command fails because the camera rectangle cannot leave the room rectangle. With your approach you would have to use a room background as big as the tilemap.

However you don't really need Game.Camera offsets for this. Use a room as big as the screen, store your own offset variables and draw the visible tiles at an offset, directly to the room background (using DrawingSurface functions).

Regarding the math side of things, here's how to code this:

Code: ags

int size[3], level[3]; // three glasses: [0] is the size 12 glass, [1] is the size 7 glass and [2] is the size 5 glass

  // when puzzle starts
  size[0] = 12;
  size[1] = 7;
  size[2] = 5;
  level[0] = 12;
  UpdateGlasses(); // call helper function that draws the glasses

Next we need a function that handles pouring water from glass A to glass B:

Code: ags

function Pour(int from, int to) { // from, to = 0, 1 or 2
  if (from == to || from < 0 || from > 2 || to < 0 || to > 2) return; // prevent errors
  int space = size[to] - level[to]; // how much space is in the target glass
  // transfer either space or level[from] units, depending which is less
  int transferred = (level[from] > space) * space + (level[from] <= space) * level[from];
  // do the actual transfer
  level[from] -= transferred;
  level[to] += transferred;
  UpdateGlasses();
}

Now all you need to do is call Pour(0, 2); to handle the player pouring from the 12 glass to the 5 glass.

This should do it:

Code: ags

// global header
import void ChangeRoom(int room, int = -10000, int y = -10000, CharacterDirection direction = -1);

// global script
void ChangeRoom(int room, int x, int y, CharacterDirection direction) {
  Wait(gvWaitTime);
  if (x == -10000) x = player.x;
  if (y == -10000) y = player.y;
  if (direction == -1) player.ChangeRoom(room, x, y);
  else player.ChangeRoom(room, x, y, direction);
}

You can now call for instance ChangeRoom(2); or pass more optional parameters, just like the original function.

Also note that in this specific case you can just put the Wait() command into on_event / eEventLeaveRoom, which should have the exact same effect.

Final note: I didn't write an extender function because I assume your game only uses one player character.

Screenshots of code... haven't seen those in a long time
Please post code in text form. Like this:

Code: ags

function abc() {
  Display("ABC");
}

Anyway, it's a very common beginner's problem: you typed or pasted the function into the script yourself and therefore AGS doesn't know it exists. You need to open the room's event pane (thunderbolt icon) and link the function by pasting its name into the field next to the event. Check the event pane in the room where it's working to see how it's supposed to be set up.
(See also https://adventuregamestudio.github.io/ags-manual/acintro3.html#adding-some-interaction)

Another way is to map the mouse position to the viewport directly. This works best if your map has a similar aspect ratio as your screen.

Code: ags

// add this above room_RepExec
int map_width = 1400;
int map_height = 900;

function MoveMap() {
  int sw = Game.Camera.Width, sh = Game.Camera.Height;
  Game.Camera.SetAt(mouse.x * (map_width - sw) / sw, mouse.y * (map_height - sh) / sh);
}

  // add this inside room_RepExec
  MoveMap();

When I click on my testing hotspot the message appears right away. Walking to a hotspot in the Tumbleweed template is implemented by calling Verbs.Goto() or Verbs.MovePlayer(x, y) iirc. In other words, the player shouldn't approach the door first.

Plus, the debug message should always appear. If your game doesn't react to looking at the door, something is wrong on a fundamental level.

To clarify, you did start a new game using the Tumbleweed template, right?
And when you check the events pane for the door hotspot, it does say "htokitchen_AnyClick" next to "any click on hotspot"?

That's weird. Let's do basic debugging first:

Code: ags

function htokitchen_AnyClick(Hotspot *theHotspot, CursorMode mode)
{

  Display("htokitchen_AnyClick called, Look is %d", Verbs.UsedAction(eGA_LookAt));

  if (Verbs.UsedAction(eGA_LookAt)) {
    player.Say("Pretty door");
  }
}

Fixing this might be as simple as

Code: ags

  // rep_exe
  if (player.ActiveInventory == null) HandleCursors();

In other words, if the player has picked an inventory item, skip the automatic cursor mode change.

However, your problem description seems to contradict that, so I'm not sure how to address this.

If you import the sprites in numerical order and use an object for the padlock dial, you can change the .Graphic property using a simple calculation.

39 frames means if you start the import at sprite slot 12, the last sprite is in slot 50. So the code could look like this:

Code: ags

function RotateLockBy(int by) {
  int first = 12, last = 50; // sprite slots
  int slot = oPadlock.Graphic + by;
  if (slot < first) slot = last;
  else if (slot > last) slot = first;
  oPadlock.Graphic = slot;
}

Put this above your arrow hotspot click handlers and simply call RotateLockBy(-1); and RotateLockBy(1); respectively.

It's weird that the player moves in one case and not the other.

Anyway, having the verbs means you're using the Tumbleweed (9-Verb / Lucasarts) Template, not the Sierra one.
In that template, a single left-click runs the WalkTo action code.
Did you try clicking on the "Look At" button first? The template also has an action line which should display something like "walk to door" when you're moving the mouse over the door.

I assume you're using the "mouse moves over hotspot" event?

Anyway, like Laura says, use a custom property. I'd get rid of all the existing hotspot events and just implement this globally.
The cursor modes all have enum/int values, so you can use these to set it up. eModeInteract for instance is 2.

So I'd add a custom property "cursor_mode" like this:

(or skip characters here if you're always showing a talkto cursor)

Next you need to track what's under the cursor to implement your own "moves over" and "leaves" events:

Code: ags

// above rep_exe
LocationType prevLocation;
Hotspot* prevH;
Object* prevO;
Character* prevC;

void HandleCursors() {
  int mx = mouse.x, my = mouse.y;
  Hotspot* currH = Hotspot.GetAtScreenXY(mx, my);
  Object* currO = Object.GetAtScreenXY(mx, my);
  Character* currC = Character.GetAtScreenXY(mx, my);
  LocationType currLocation = GetLocationType(mx, my);
  bool isH = currLocation == eLocationHotspot, isO = currLocation == eLocationObject, isC = currLocation == eLocationCharacter;
  bool typeChange = currLocation != prevLocation;

  CursorMode newMode = eModeWalkto;
  if (isH && (typeChange || currH != prevH)) newMode = currH.GetProperty("cursor_mode");
  else if (isO && (typeChange || currO != prevO)) newMode = currO.GetProperty("cursor_mode");
  else if (isC && (typeChange || currC != prevC)) newMode = eModeTalkto;
  
  if (newMode != mouse.Mode) mouse.Mode = newMode;
  prevH = currH;
  prevO = currO;
  prevC = currC;
}

  // inside rep_exe
  HandleCursors();

If most of your objects are supposed to show a pick up cursor instead, create two separate properties and use the 2nd one for objects with a default value of 5. This also requires changing the GetProperty string in the object line above.

The formula seems to be:

Code: ags

  int gameloops = ((StrLen(text) / game.text_speed) + 1) * GetGameSpeed();

https://www.adventuregamestudio.co.uk/wiki/AGS_tidbits_%26_snippets (about halfway down)

game.text_speed has a default value of 15. So 15 characters are displayed for two seconds, 30 characters for three seconds, etc.

Judging from the screenshots of your inventory GUI in the editor, I don't think you've actually used the new background with the border?

For me it looks like this:

Can you describe how it's not working?

I did a test with the Sierra template.

(This template has the inv GUI set to "pause game when shown", which will prevent rep_exe code from running, so this might actually be a much easier way to solve this.)

Anyway, I added a transparent border to the background image png, changed the position and size of the GUI accordingly and moved all the controls to their proper spots.
Then I used this code to display the hotspot's name in the status bar:

Code: ags

// called on every game cycle, except when the game is blocked
function repeatedly_execute()
{
  String name = Game.GetLocationName(mouse.x, mouse.y);
  lblOverHotspot.Text = name;
}

The transparent background prevented this mechanism from displaying the hotspot's name while the GUI was open, so it worked as expected. I.e. a transparent but clickable GUI catches room clicks and GetLocationType / Game.GetLocationName.

One easy way to fix this is to make the GUI as big as the screen and use a background image with a transparent border. A clickable GUI will prevent the cursor from reacting to hotspots even if the background is completely transparent.

Another way is to check if the GUI is open before changing the cursor. Is this done in repeatedly_execute code? Or are you using the built-in way (AnimateOnlyOnHotspots)?
If it's the former, you can just wrap the code in

Code: ags

  if (!gInventory.Visible && !gInterface.Visible) {

and

Code: ags

  }

Edit:
I'm now sure I misunderstood the question. Removed my initial answer.

So do you mean like disabling certain verbs altogether until the player learns how to push stuff for instance...?
To make a button invisible at the start of the game, open GlobalScript.asc from the Scripts node and go to the game_start function. Now put this command inside the function:

Code: ags

// called when the game starts, before the first room is loaded
// =======================================================================================
function game_start() 
{
  SetRestartPoint();
  btnVerb7.Visible = false;  // add this line
}

To show the button again, just set it back to "true".
To find out which button you need to address, open GUIs -> gMain and click on the button once. This will show its script name at the top of the properties pane.

(IIRC, translating your game to another language might actually change the button that is used for "Push", but this should do for now.)

The correct time to learn how to use variables is always yesterday, because it means you can suddenly solve 99% of your problems today

Seriously, don't put this off. Adding a global variable is very easy thanks to the project tree node of the same name.
Create an int named pizza_state with an initial value of 0.
A value of 1 means the pizza was ordered and has appeared in the other room. A value of 2 means the pizza is gone again.

Code: ags

  // ordering pizza
  if (pizza_state == 0) pizza_state = 1;

In the other room's room_Load:

Code: ags

  oPizza.Visible = pizza_state == 1; // turn object visible if state is 1

When the pizza is taken:

Code: ags

  pizza_state = 2;
  oPizza.Visible = false;