it's a tom thumb snaffle with a roller, not a pelham. it's a western bit meant to be used with one rein, a pelham is an english bit meant to be used with two reins. it's a curb, unlike its name suggests. the roller softens the bite of the broken mouth just a tad and discourages a young horse from putting their tongue over the bit, the grazing shanks are a tad less severe then straight ones. most western people think a tom thumb is milder than a ported bit, but actualy it's a double action bit that can put a viselike grip on the mouth. i personaly never would have started a baby in one. that said, if he likes it, leave it, i'm a huge believer in the ain't broke/don't fix it theory on bits. i have tons of bits, my favorite is whatever works on horse i'm sitting on. make sure it fits, width and thickness, and use what they like.
as far as riding goes, three hours is a very long time for a two year old. i would keep it 10-20 min, certainly under a half. there's a reason everyone is saying "baby". he's still growing, bones, muscles, ligaments, tendons, and brain. he dosen't have the mental capacity to focus that long, he dosen't have the physical developement to carry you that long. he might be very well mannered about it, yet in a few months you're going to be wondering why he's slightly off one day, you might notice he's not so good natured anymore, or you might notice something sooner, bucked shins, hot knees....he'll get a sore back, and rightly associate that with riding, there goes the attitude. you wouldn't jump off a couch and run a marathon, don't expect him to. even just sitting on his back that long, he needs to slowly build those back muscles. baby's don't just need training, they need conditioning, slowly and continualy, and he'll still be going strong at 10 and 15.
edited to add: you should be NECK-REINING in this bit not direct reining, no pulling left and right, it's not designed for that. play with it out of his mouth to see what's going on in his mouth when you pull this way and that.