There are jillions of undermount sinks available. Maybe shop at Fergusons; lots in their catalogs.

The holes depend on the sink. If you have a sink with a faucet deck that's exposed, the deck will often come pre-drilled. It isn't hard to drill a sink if you want more. If you have a sink with no faucet deck, the fabricator will drill the top as necessary.

If you are replacing your cabinets, you can get a full apron cabinet and a full apron sink. If you're not, you have to get a short apron sink which is designed to fit in existing cabinets.

Thanks Joseph for the advice and recommendation. My husband and I actually went ahead to make an appointment at the Fergusons near us next week.