There's only 3 active right now. There isn't any difference between them except for channel 1, which is the Dragon Ball Scramble channel. You must be at least lvl 46 to participate, but any level can be in the channel. Usually I will play on the most populated channel when looking for PTs for dungeons or TMQs. When I am questing or farming DBs, I tend to do it on the least populated channel.
Kinda think of them as servers within the server. You can still talk with anyone in any channel, but you wont be able to group up with them unless you're in the same channel
Time Machine Quests. You'll find the first one in the second map. I wouldn't try to get into a pt until around your mid 20s. Do them until your level 31. If you can, save your quests and try to do 10 TMQs a day. The less you spend questing now, the more you'll be able to do later when some levels don't have many quests.
Also, make sure you get a set of legendary armor. You'll know it when you choose your reward and there are only 3 pieces of gear (If you don't have an English patch, the name of the armor is in purple).