in "arbetar", is the accented syllable ar or be? in other words, is it ARbetar or arBEtar?
I'd say it's just that some nouns have på, others have i. Some may have both with different meanings. With a bank (an ordinary 'money bank') the preposition is på for most things. Definitely for working there, but also for Hon har pengar på banken 'She has money in the bank'.
I would say that it is. Was it marked incorrectly? Swedish doesn't need to distinguish these. Most of the time though, you would say in English "She works in a bank" because you're telling someone where she works all of the time. If you just want to say what they're doing now, you wouldn't include the "in the bank." "She's working in a bank" makes me think that she doesn't usually work in a bank but she is now.
That could feasibly mean a number of different things and not like the sentence above.