1. I believe that age 2 and older need a ticket. If you have a small/young 2yo, you might be able to get away with no ticket but that's on you to decide. It might be worth buying a ticket in order to have some extra space.
2. It really depends on the child and it depends on the fan. Most 2yo's don't sit still very well and the sounds and lights and action can only keep them entertained for so long. Also, if you want to focus on the game and watch it intensely, you're going to have a problem. My wife and I took our kids to games when they were that little and it didn't always go well - a lot of time spent in the halls, not that much time focusing on the actual game. Don't get me wrong, it's fun to experience a game through a child's eyes, but I'd recommend taking your kid to a no-name, non-conf game. The crowd is smaller and the games are typically less exciting so leaving early is no big deal. Also, DVR the game
FWIW, I have 7yo twin boys and they've been all about MU basketball since about age 5 (i.e. once they could read the names and scores). My 5yo daughter is less into it, but she's willing to go, eat popcorn, find the mascot and scream with excitement when the stadium gets loud. The 3yo prefers to stay home.