It's a good idea with a new pet to find a suitable vet and get a wellness check. Do you have a rabbit vet in your area?

Do you use any wood based litter or bedding? Maybe that's irritating the eyes?

The tummy can make noises but quiet ones. You shouldn't be able to hear it across a room, for instance.
Do you currently have the rabbit eating the same food he was getting before? It's better for their stomach if you slowly transistion them over into new foods.
It's good he's eating normally. Be sure to check he is also pooping. Very important.

Hi, Candace,
JG is right, it is really important to get started with a new vet for your new bunny so you have a baseline exam established, determine whether you like the vet before you have any sudden need, and know how healthy you new little guy is. If you look at the top of the Q&A forum, you'll see posts for finding a good vet in your area. Exotics are what bunnies are listed under by most vets. A watery eye can be an indication of several issues, sometimes teeth problems, or blocked ducts, or allergy to something like your choice of litter. Have him checked.

Also, read over the Bunny Info. sections thoroughly to set his habitat up in optimal conditions. For example, they do not need bedding, just litter in a litter pan. And never use cedar or pine shavings. Stuff like that.
Oh, and we like to see photos!

Welcome to Binky Bunny.

My Mini-Rex developed watery eyes on several occasions. Not sure what the cause was but it took drops from the vet to clear them up. Like RabbitPam mentioned, teeth issues can cause watery eyes and dwarf bunnies are particularly susceptible to teeth problems. Best to have a vet check him out.

This is definitely something to bring to your vet's attention. Your vet will do a full exam and check his eyes and teeth.