WARNING: DH SPOILERSWhat do you expect him to look like? I've given him his father's hair and his mother's eyes, but I'm not sure really.
Yeah, what you've given him is fine. 'Cause he's a Potter and should have the famous black hair. Even in Philosopher's Stone, in the chapter 'Mirror of Erised', Harry sees men who have black stuck up hair, so it runs in the family. It's mentioned in DH that only Albus inherits Harry's eyes, so most probably James would have brown (Ginny's). And, i don't think that any of the Potters were supposed to be 'hot' so James won' be either considering that the Weasleys aren't exactly good looking too.
Do you think he'd be into pranks like his grandfather and uncles?
Of course! It runs in the family. Both the families as a matter of fact. So obviously he would take up after them and be like the Marauders.
What kind of relationships do you think he'd have with his friends and family? We know that he and Albus are quite close, but what about the rest of his family, like his sister and his parents?
He'd be really close to them. Fine, he's not the sentimental and all type, but he does love them. We can make that out from the Epilogue.
Do you think he'd be very similar to his namesake, and how do you think he would feel about him?
Yeah. Both were fun and naughty and loved to play pranks. We see James Jr. teasing Albus in the epilogue, so we know that James Jr. was like his grandfather. James Jr. wouldn't know much about his grandfather. Harry didn't know much about his father, except what he got to know from Dumbledore, Sirius and Remus, but neither of them are alive when James Jr. is born. So he probably wouldn't know much about his grandfather except the fact that he was really mischievous and all. So most probably he would want to follow his grandfather's footsteps.