Okay, I'll tell you everything that I know. ^_^; It just started showing here last November, and we haven't gotten too far into the series yet. The questions/rumors are in bold, BTW.
1. May is twice as dumb as Ash
That's not really true. She's just a beginning Trainer and doesn't know that much about Pokemon.
2. May dislikes pokemon battles but enters Pokemon contests.
That's true. At the beginning she tells us that she doesn't really like Pokemon and battling, but later on when she sees a Pokemon Contest, she decides that that is what she wants to do! So, now she does enter them and instead of collecting badges, she collects the ribbons. This also made her seem to appreciate her Pokemon more.
3. Max goes to Pokemon school in Rustboro
I don't think this is true. Maybe he did before joining Ash and co., but not while they're traveling. If you've seen pictures of Max doing some sort of schoolwork, it from an episode where they all visited this Trainer school that Roxanne teaches at.
4. What are their personalties?
May is a lot nicer than Misty was when she met Ash. She doesn't have as much of a temper, and seems to look up to him more. Though, she can get easily annoyed by her brother, Max. So basically she's a friendly, outgoing person. She loves shopping, especially for swimsuits, and often ends up getting tired or hungry during their journeys. Funny though, she claims to just love traveling, but she isn't a very good one sometimes. XD
Max is almost the total opposite of May. He thinks he knows everything, especially about Pokemon, and corrects May or Ash whenever he can. He's still nice though; he just easily gets his feelings hurt. He's also a bit bossy at times. But, he's still young so he's a lot more immature than the others.
1. Is May the new Misty?
A lot of people think so, but who knows? Misty does meet back up with everyone and stays for about two episodes, but then she leaves back for Cerulean City. So.. only time will tell who will stay with Ash forever.
2. Anything that May or Max like / dislike?
May:
Likes - Traveling. Training Pok?mon was just sort of her excuse to travel around to different places.
Dislikes - Pokemon, at the beginning of the series. She just wasn't interested in them.. until she found out about the contests. =P
Max:
Likes - I don't know much about his interests, except he enjoys studying Pokemon, and his Pok? Nav.
Dislikes - Probably just being wrong. He's the kind that can't really take it too well. ^_^;
3. What's Max's reason for joining Ash's group?
While Ash was visiting the Petalburg Gym, where he lives, Max kept hinting around about wanting to travel, etc. Right before May and Ash left, Norman (their dad) asked if it would be alright if Max came along too. Their mother seemed to like the idea too, (so she wouldn't have to worry about him) and everyone else agreed, so that's it! Norman also gave Max a Pok? Nav, and May and Ash got two badge cases.
I hope this helped. ^_^ If you have any more questions then feel free to ask! By the way, I'm going to move this to Pokemon TV Shows and Movies. It's more related to the Anime. *moved*