If you say 'Was he once a teacher?', you mean 'He was a teacher at SOME point in his life, wasn't he?'. You suspect that this is true, and you are looking for a confirmation of this fact. Perhaps you have noticed how good he is at explaining things, so you presume that he has teaching experience. If you say 'Was he ever a teacher?', you mean 'Tell me if he has been a teacher at ANY time in his life'. This could mean that you have no idea, or it could mean that you suspect that he has never been a teacher: 'He has never been a teacher, has he?' You might like to take a look at the Discussion which I initiated yesterday (https://www.italki.com/discussion/199886), as it deals with the same issue. The difference between 'something' and 'anything' for objects is the same as the difference between 'once' and 'ever' for times.

Yes, they both mean the same thing, and your answer to the question is perfect.

In my opinion NO. Frequently "Ever" we use it with verbal tense: the present perfect, in question for example: "Have you ever been to France?" . I suggest to verify a Phrasal verb, Let's see others opinions here.