While it would be difficult for me to fathom some theories as to what Chomper might have done, I can definately point out what the movie proves he does, and based off the facts it provides, I can add some educated gueses which could very well explain some things. It is clear that Chomper spent a lot of time exploring the island and even naming the places, something he still needs to work on. But most interesting of all was the fact that he analyzed the importance of the places he finds. Remember when he hid his friends in the "Stinky Place?" He put them there because he understood that sharpteeth could not find them because of the strong odor of the plants there. While it is possible his parents simply told him about smells confusing sharpteeth, for the sake of making things intersting, I have some theories as to what personal experiences might have happened to make him realize that.
1. His parents were looking for him, and as children are playful, they like to hide from them at times, and perhaps Chomper- being a child- does just that by hiding in the 'Stinky Place" not even realizing what would happen, it was probably just a nearby place to duck into. When his excellent tracking parents walk right by without noticing him, he could probably piece together what happened.
2. Or maybe somthing simpler. He is hunting small prey, smelling it with his mouth watering, when it jumps into the "Stinky Place" and the scent vanishes. Another easy discovery.
3. But what if discovering this wasn't so easy? With an island full of exotic smells, he might've noticed his sniffer not working so well near them. Then he finds the "Stinky Place" and makes a realization, "If my sniffer has trouble with things that smell half as strong, it musty be impossible for sharpteeth to smell around here!" A little bit more thinking is involved on Chomper's part here, but he's a clever little guy.
As for friends, I highly doubt he had any. On that very small island, you'd think any friends would be hanging around. For the two days the gang is there, Chomper is not seen interacting with any one else his age, and it seems odd that he would ignore any old friends when new ones came. Chomper was dying for the others to meet his parents. Usually kids want friends to meet friends. I usually only see such an effort to introduce family when there is no one else around to introduce. Littlefoot says, "So, do you live here?" "Yep. Me and my mommy and daddy!" he answers. He doesn't mention anyone else. Think about it. If you lived with a friend and your parents, and somebody asks you about living where you are, why on earth would you mention your parents and say nothing about a friend? I highly doubt Chomper would have forgotten having any other friends. Call me crazy, but I don't think he wanted Littlefoot to stay because he's a friend that he can play with. I think Chomper wanted him to stay because he's Chomper's only friend, the only one to play with.
I figured he go hunting with his parents and maybe by himself.
I can give a confirmed response to that. It shows Chomper hunting by himself toward the beginning. He finds the gang because he was hunting them. It wasn't originally a friendly visit. He chased them with a death glare that only went away when he recognized them. This also proves that had gone hunting with his parents in the past because they must've taught him what do. He didn't have a death glare until he left with his parents.
As for life in general, young children need friends to play with, and Chomper had had a taste of true friends as a baby which turns out that he did not forget about. Therefore his life was as lonely as possible. If he had never had friends, he wouldn't feel as bad since he wouldn't know what he was missing. But after taking one bite of candy, even if you can't get any for a long time, you never forget the pleasaure it brought you, and therefore you suffer, because you know how good something is, but are only being able to enjoy it in your dreams. And I'm not saying Littlefoot ruined his life in any way. You know what they say, "Tis better to have experienced true friendship and lost it, than to never have had a friend at all." Okay, that's not how it goes, but I had to make it fit. Chomper was lonely, but I believe knowing what is out there and longing for it beats being oblivious to the worlds pleasures any day.