It won't let me set up a home for my villager, even when we're married.

What happens if you do so? Anything in the chat?

yes, she asks me if there is another place nearby and some other things

Then the building is not valid. If you use the blueprint it tells you more detailed reasons. Or you can wait for 7.4.0 since that removed the need of valid buildings.

Can I change the version without my villagers disappearing?

In some cases, but most of the time, no.

Upgrading should always be fine

Closing as technically resolved, 7.4.0 will have a better system, but for now the blueprint rules us all!