From this point he sticks around, and his identity is slowly revealed to everyone. In other words, the fact that he's Vegita and Buruma's son. I don't normally go into this much detail, but I'd say Trunks is a pretty popular character, and this should answer most of your major questions about him. As a person, Trunks is fairly quiet. He doesn't say much except when he has something VERY important to say, or he's invited into a conversation.
Trunks use a formal type of language.
Even when fighting Cell, he keeps his cool and carries on a conversation with him. It's safe to safe that he's the type of person who would be willing to sacrafice himself so that others could live. I've been waiting to do this one, because I want to kill a myth which seems to be spreading. They say he's a complete contrast to Future Trunks, yadda yadda yadda. That's not true.