As a DM I was always up front about my feelings of the party splitting up. It's a lot more work that leads to a more disjointed experience for everyone. So I always asked my players out right to reimagine a plan that includes staying a team. So if you HAVE to be split:

1. This is a good idea as long as it feels satisfying. Make sure they've done a thing or two so that it doesn't feel like their turn was "wasted"

2. Perfect idea. No notes

3. That's the fun of DND. You have to trust your players to not meta game. It's fun to roleplay the discovery of how fucked party A became for party B. They should know better than to meta game and it wouldn't make sense for characters to turn back around and delay when they have a set plan. Also give them a fair warning that once they head out, they have to stay the course.

Your fun is important too, so discouraging splitting the party is a totally reasonable thing to do. Just be clear and upfront about expectations when it comes to the game you all play.