Can Grace be irresistible and still be a gift? According to TULIP Calvinism grace is "irresistible".  If grace is irresistible then what role does faith play in salvation and can it still be considered a gift?
Yes, salvation can still be considered a gift.  In general, something can be considered a gift if it:


Is positive/desirable
Is given rather than earned (otherwise it should be called a wage)
Is given without obligation of repayment (otherwise it should be called a loan)


Whether a gift can be resisted or not has no bearing on its "giftiness".  According to Calvinism, faith comes into play as the mode with which we receive the gift of salvation. So, in order to cause us to be saved, God regenerates us and then causes us to have faith.  

The irresistible quality of the process (regeneration and subsequent faith) does not undermine it's "giftiness".  On the contrary. According to Calvinism, salvation would not be purely a gift if it were resistible, because then the act of choosing to not resist the gift could be construed as meritoriously earning it, at least in part.