Here are some resources that will help you determine when you can expect new queens to emerge and start laying:

• Help! I need a queen! by Meghan Milbrath
• Beekeeping in Northern Climates Manual from University of Minnesota Bee Lab

1 hive had an uncapped queen cell. I don’t know if it ended up in the split with the queen, since I never found her. How long do I have to wait, before I can open the now 2 hives to see if they ended up together?

If you're careful to not jostle or tear open the queen cell, you can check the hives that may have ended up with the open queen cell before a queen is due to emerge. The pupal development of queens is 8 days, so you can figure that you can check the hives within a week of when you saw the open queen cell. If you find eggs in one of the hives, you will know where the queen ended up.  We generally want to avoid checking hives with new/virgin queens to avoid disrupting them. If you're at the point where one of the hives may already have a new queen, I suggest waiting at least a week from when the new queen to emerged to check the hive.

Question 2. Another hive had several queen cells that were capped when I did the split. Again I couldn’t find the queen, but this time I removed all the queen cells, figuring whichever hive didn’t have a queen could make another one. Was this the correct way to do this?

If there were capped swarm cells and you didn't see the queen, it's possible that the colony had already swarmed. I've found colonies that are huge in population that have already issued a swarm, so assuming the colony hasn't swarmed based on population size isn't foolproof.

Were there eggs in the hive? The queen stops laying as the colony prepares to swarm. If there weren't eggs (or very young larvae) when you split the hive, then they may not be able to raise a new queen.

I suggest giving both these hives a frame with eggs from another colony and checking back in a few days. If they raise queen cells, then they are likely queenless.

Happy beekeeping!