I don't really care about the inventory or the family funds, I also already found answers to this on the internet. I believe the game also tells you that when attempting to move out a family. That the relationships will be lost is clear, too.

What I do care about is the process of my game. There is this new stuff with the opportunities and Oasis landing, and you can "unlock" a lot of things.
I want to move my single Sim who is living in Isla Paradiso to the library, replace the world with a fixed version (http://modthesims.info/d/514909) and move her back in where she was in the old world.

1. Will the game give me opportunities I already completed again?
2. Does she lose her job level through losing the workplace, since I practically move her out of the world where it was? Means, do I have to find a job and start the career at level 1 again?
3. Does she keep skills, memories & inventory?
4. Will the game recognize I already completed the opportunity that lets me travel to Oasis Landing (finding the batteries and talking to the time traveller), and that I already did this "find Skippy" stuff that you get when you first arrive there?
5. Will she keep her wardrobe? It contains like felt 34672938475 outfits with help of the dresser mod.

(Plus:
Does the game recognize Oasis Landing as some sort of subhood to every game? Means, do you get an exact copy of that hood every time you start a new savegame, so it only looks like it's the same one everywhere, but it actually is the same one if you just switch the active family inside of one savegame? (That's just because I'm interested in how this works.)

Some things will be lost but most things will be kept.

1. The opportunity history of your household should remain intact, i.e. if you've received and completed the Oh My Ghost! or the Omniplant opportunities, the Sim will still be able to resurrect ghosts and order Omniplant seeds. Also all WA adventures completed will still be listed as completed even though in the new neighbourhood the tombs will be fresh again. But you cannot receive these adventures anymore.
2. She will only lose her job level if the work place is missing in the new world. Otherwise everything will remain at the same level. Her job performance at her current level will be reset to 0 again, though, and school children will start with a C again.
3. Yes she should keep everything. Some skill challenges will be reset, however, like Super Friendly or Everybody's Best Friend. But collection statistics and handyness upgrades etc. will still be marked as completed.
4. As soon as the portal arrives (if you import her with her house the portal will still be on the lot, btw) you can "Inspect" again, but this time the time traveler will not come and you can travel to the future immediately. As regards the future opoortunities, hm, I don't know. I think my bot builder lost his legacy statue in any case.
5. Wheter she keeps any outfits above the regular 3 possible ones per category, well, you'd have to find that out yourself. The special outfits (scuba diving, costumes etc.) might end up broken though. Overwatch fixes some but not all of them.

(Inside one savegame Oasis Landing will remain the same. If you start a new game and travel to OL then this will be a fresh version, just like the WA worlds and the Uni world)

OK thanks, I did it now and everything is fine.

I was about to ask the exact same thing, as I want to install fixed worlds as well. So thanks for the answers! But I have one more question. I'm playing a Legacy, and I'm at the 2nd Gen. now. I want to move the entire family into the library, then start a new save for them. But will the family tree remain?

I think they lose relationships, which should also include family ones.
The porter should be able to keep them tho:

https://nraas.wikispaces.com/Porter

Thank you, I didn't know about that one!

If all of your family live in the same house, they will retain their relationships (and everything else mentioned above) when you save them to the Library/Bin. If you save them under different or multiple household saves, they will lose their relationships. In that case, NRaas Porter is one of your best friends.

Not sure if this was a glitch or not, but the last time I moved a family to a different neighborhood only parent/child relationships were kept. I had 2 parent sims, their child, and one of the parents had a sibling. The sibling was listed as a roommate after I moved them and their relationship went back down to acquaintances. All of the sims were in the same household, by the way.

oO It wouldn't make a sense to me if it is suddenly supposed to be like this in Sims 3... but then again, that never seems to be a point as for Sims

Traveler also has some options for Switching Homeworlds if you prefer not to use Porter. It's a good idea before using any of these to make a back up save of your current game so you can go back to it if something goes wrong.