People have done it. The rules technically say you need to be in the country you are applying from for the duration of the application.
As others have said they may ask you for an interview or copies of every page of your passport. If you can’t attend or provide those they may see that you are no longer in the country and can cancel the application.
Your call. You can try. You might get lucky. You might not.
Depends how the daughter entered Thailand. If with a Thai passport then they are treated as a Thai national. If using the EU passport then they are treated as Non Thai and the father could get a guardian visa based on the daughter being at an international school.