at the moment = present tense "for a year" cannot be used with the present tense.

Here the tense 'is working' is a continuous one ,so it is more appropriate to use 'at the moment'.

If you want to say that tony is working at the bank and started working there a year ago, you would say 'Tony has been working at a bank for a year'. The present continuous tense implies that he worked in the past, is working now and may be working there in the future.

I think b) is OK but it changes the meaning. Maybe Tony's plan is to work at the bank for only a year. We certainly can and do use "for" + length of time with present continuous. I'm visiting L.A. for a few days on business. He's staying with us for a week before he goes back home. They're working from home for a few days while the office is being renovated. etc.