Could you add to the port, a virtual screen keyboard that pops up, if i open save game menus?
I doubt it is possible to detect when savegame menu is on, because for the engine all menus are the same (unless the game uses default built-in AGS functionality, which is not very common in latest games).
Probably it would be possible to detect when a text input control is shown and has focus.
Still, this won't help in exceptional cases when game has some custom way to program user input. Therefore, I am wondering if it would be better to bind virtual keyboard appearance to any of the persistent device's controls?
If you don't type anything name the savegames save[$]
Again, that depends on the game. If the game does not test for empty string and tries to save game even with empty name, then engine will be able to hack in and change that name, but if the game is scripted in such a way that it checks for empty string and does not let to save if string is empty, then not much may be done...
To summ up, since the engine is a "virtual machine" which executes scripts, in most cases it has no means to "understand" the meaning of script actions as we, users, see it and find the ways to override it.
Unless the overrides are programmed on per-game basis, that is.