After I degrease chain with mineralspirits, do I "have" to remove it by rinsing before oiling, or can I let mineralspirits evaporate, then oil chain?

Mineral spirits will evaporate on its own. It doesn't take too long. Even if you oil it with some MS still present, I don't think it'll hurt anything given that they're both oil based.

An hour in a reasonably warm room with the chain sitting on a rag should be more than enough time.

After degreasing, I'd rinse a couple of times. But by rinse, I mean just repeat the degreasing.

It's bloody hard to get all the crud out of a chain.

Getting the spirits off, evaporation will work. But if you dry it with a rag, you'll get some more dirty crud that was left on the chain and still suspended by the spirits.

(Of course, the mineral spirits will help transport the new lube inside the chain, so it may not make much difference in the end.)