Small layover time. What to do?

If your two legs are on independent tickets, they won't care, and are not obligated to either.

If it's on one ticket, they have to take care of you and make sure reach your destination. That will naturally include getting you a ticket for another flight (which may be with another airline).

If there's a night in between they also should get you a hotel room, and directions/transportation (if it's sufficiently far away, hard to get to with public transport - they might have to imburse you for that) for getting there. If they won't allow you access to your checked-in luggage, I think they also have to give you a toothbrush, and perhaps a few other things. But airlines (I have no idea where AI is on the scale) have been known not go give you more than you ask for. A couple of years ago, some friends of mine were on a delayed flight from CPH to LHR, so they didn't catch their flight on to HKG, and as they described they a lot of trouble getting BA to get them a bus to the hotel (I believe the hotel at LHR was full, so BA got them rooms at LGW). If you've got the time try reading a little about the rules you think might be relevant, and if you need to (let's hope everything goes smoothly) be reasonable but firm when you talk to the ground staff.

If it is on one ticket, yes, they will rebook you for free (and handle the luggage accordingly).

If you bought two independent tickets, you are on your own.