The Hotspot does not appear, but when I click with the eye over it, AGS ends with an error message
I think I've dealt with that before but could you explain a little better?
Maybe reporting the error message? And telling a bit more specific what you were doing, what was supposed to happen, and what happened.
When the new game screen comes up there is no New Game icon. What should I do? :-\
Re-extract the files to a different folder (from the zip file you downloaded).
Perhaps something was deleted from the first folder?