Can I use a Gift card & avail an offer in one transaction?

You would be unable to use a Gift card and try availing a Debit/Credit card offer simultaneously. 

To avail, any Debit/credit card offer the payment needs to be made via the respective card.

You CAN avail non-card/Cashback offers with the gift card.

All you need to do is apply for the gift card first and then make the balance payment with the desired cashback/non-card related source.