This isn't so much a question as a quick verification, but still: since it's permissible to move an sim into a previously empty home in order to start a new household, this is presumably an exception to the rule that says I must "immediately put them in any home" - if done through Manage Households, the sim in question has to briefly be Not In World in order to form their new household. Thus, as an example, if I were to move Summer Holiday out of the BFF household, I would have to immediately select her new Holiday household and then "Move Household into a lot" - it would clearly not be okay to leave her Not In World while I moved Dennis Kim out of the SKLs and into hers.
The key is that all moves have to made in one session in Manage Worlds/Manage Households. The order doesn't really matter, you just can't to back to Live mode and then go back into Manage World/Manage Households to make more moves with the same sims. Please let me know if this is still confusing.
[Are there any restrictions on the amount of cash a sim can move out with? For instance, if Jacques Villareal does a runner from his kids, leaving them to fend for themselves on the Von-Windenburg estate, could he take all of the Villareal household's initial §65,000 with him?
No restrictions on how much money they take.
When a sim moves out of their original household and into a previously empty home, must they buy it furnished or can I select "unfurnished" instead? Since no structural changes are allowed, bulldozing is obviously a no-go, but since selling objects in the home is permitted in the main...
They do not have to buy it furnished.
Is there any obligation to play a sim after moving them out of their original household? For instance, say Vivian Lewis decided she needed some peace and quiet in her final ye- uh, days; could she buy Crick Cabana and enjoy a pleasant retirement there without me ever having to bother her?
There's no rule that you have to play a sim that you move out, only that you have to move them into a house.
If there's still an empty space in a household after I've moved on from it, can I move a sim from a household I'm about to play into this space using Manage Households, a process that would not require that I play the household for a second time? Example: suppose I force the Pancakes to have five babies, then decide my work there is done. Back in Manage Worlds, I look at the SKLs, and see that Vivian is still alive. In this hypothetical she doesn't get a peaceful retirement; rather, I use Manage Households to put her in with the Pancakes, then continue on with the SKL household.
A sim that you want to move out can be moved to any household, including one that you've already played.
How do I treat the premade sims that live in university accomodation? They form two households (Fletcher for Cameron Fletcher and Best Of Friends for Julia Wright & Becca Clarke) and aren't technically homeless, but since you cannot use Manage Households to move sims into university lots outside of enrollment, they would have to use their one permitted move to go off-campus... not to mention the fact that they can't adopt/get pregnant there...
They are considered starting townie sims because they are there at the beginning of every game and living on a lot, but as you said, they would only get one move to an off-campus lot and then couldn't move again.