I love doing character meets!
It's totally fine to ask for a pose (as long as it's not inappropriate). Just say, "Can we do..." Like, for Peter Pan, you could ask to do a flying pose, or ask Cinderella if you can show off your shoes together. If there's a special picture you want, you'll be disappointed if you font get it, so just ask. I've asked for things like an over the shoulder shot with Pocahontas (to show off that we both had long hair), etc. That's not a pose the character or photographer regularly suggests, but it was one I really wanted because she's always been one of my favorite characters and I love having long hair like hers.
A couple caveats: First off, if it's something out of character, they might ask you to teach them first, or to do it on your own and they'll cheer for you or do a reaction pose. For example, if you ask Lilo to "hang ten", she'll know exactly what you're talking about, but with Aladdin, you might have to explain that surfing is like riding a magic carpet, just on the water instead, and show him how to pose first. Second, one special shot in addition to what they do automatically is fine, but please keep it to one, *maybe* two extra poses. I've had people in front of me do what felt like a whole photoshoot with the character, doing tons of different poses and swapping out members of their group back and forth so that they took five times as long as any other family in line. That's frustrating for everyone else waiting to see the characters, especially when they're only available for a short time. So be mindful of others, but don't feel like you have to rush, either - you have just as much right to visit the characters as anyone else.
You can also ask questions about their stories, like how Rapunzel grew her hair back out after Flynn cut it, or whether Merida thinks her brothers were more trouble as boys or bears. But don't try to trip them up with actual plot holes or anything that's meant to try to trick them.
If you want the characters to hold something with you (like a sign that says "Best Day Ever" or whatever), they'll likely be willing to do that, although there's still a chance they'll politely decline or try to suggest something else to do. They're probably much less likely to be willing to wear something that isn't part of their costume, and, again, if they're not okay with it, they'll find a way to politely decline ("Oh, my prince loves wearing glasses like that, but they don't match my dress, do they? Why don't you wear them instead?") If that happens, don't try to push the issue - a polite or indirect no is still a no, and they're just trying no to do anything they shouldn't.
If you're really unsure, just ask one of the line attendants before you reach the character, and they can give you an idea whether it's likely that they'll be okay or not. Just something like, "Do you think Jasmine would be willing to hold this teddy bear for our photo?" It'll still be up to the character in the moment, but the attendant can at least let you know if it's totally out of the question or not.
I hope that helps some!
PS: On the tipping issue, I know tipping (at least in the US) can seem kind of random at times, but as others have said, no, tips aren't expected or needed for anyone inside the parks except waiters at table-service restaurants. No need to worry about it.

[But there's no shame in asking when you're not clear about something.]