Yay, EA came with an update!
Haven't tried it yet, but they say to have fixed many of our problems and I quote:
Game Update 1.47This game update includes the following changes:
Base game updates:
•Fixed an issue where Sims could not get married.
•Fixed an issue where Sims could not use the telescope.
•Fixed an issue where Sims could not collect space rocks.
Create a world updates:
•Fixed an issue with saving worlds in Create A World.
•Worlds will now install and appear on the main menu properly when downloaded. Worlds do not need to be resaved for this to apply. Any worlds that were affected by this issue can be reinstalled via the launcher and will appear in the main menu.
Store updates:
•Fixed an issue where several Store sets were not appearing in the appropriate room category in Buy Mode.
I sure hope this will fix the problems with installing and saving UC!
Edit: Yes, it worked! After the patch, just install the world from the launcher once more and you're done