"My father watches TV in the evening." is correct. This means he watches the programmes shown on the TV. If you say "My father watches the TV in the evening" (it's also correct), it means he is watching the object (the television).

Hello! In this case no you do not put the 'the' in front of the word TV because you are not directly referring to the TV as the subject. One case where you would put the 'the' in front of the word TV would be for example 'he sits in front of the TV' I hope this is clear and helps you! If you have any question please don't hesitate to ask!

It's correct. Use the word "the" when there is only one of that item in the world or the area you are writing/talking about.