It's implied in the OP too but there's a seperate Initiative check for every single Move Order. So assuming everyone uses all their skills together it will first go to Order 1 and check Initiative. The one with higher Initiative moves, then the opponent in move order 1 uses his. Then the same process happens for order 2 etc. It doesn't matter if your character in Order 2 has higher Initiative than the opponent in Order 1, the opponent takes priority cause he's at an earlier Move Order, that's why you don't see a whole team move before the other. If though you use let's say the Mysteries at Orders 1, 2 and 3 and your opponent only uses his 4th you'll see your team use all their mysteries(except for 4) before him/her.

Yes, what you're describing is entirely possible.