If it’s få that confuses you, one of its meanings is may.

You could also replace “Can I” with “Do I get to”, which might be less confusing ;)

I think we have pretty much the same situation with these verbs as in English – there's this example often quoted (when discussing the English verbs), where the pupil asks Can I go to the bathroom? and the teacher answers Well, can you? – the teacher would like the pupil to say May I…? but in practice, that is not how the language is used, people do say can to mean may. Same in Swedish, in theory kan should mean 'am able to', but in practice it's used to mean the same as får too.

Kan is like 'am I able to/capable of...', whereas får is like 'do I have permission to...'

No, that would be like "Am I capable to ask him?" in english

The verb question is either ifrågasätta (if you mean as in 'put into question') or förhöra if you mean it as in 'interrogate'.