New world objects will not generate in areas that were generated pre-patch.

The only new things you might see in old areas are mobs, so long as their spawn conditions don't have dependencies to any other structure/object.

E.g You can find abominations in old areas because they can spawn anywhere that is Swamp. But you wouldn't see growths spawning in Plains without a tar pit.

Since the game first launched on Steam they have made old maps forward compatible, as in they will still load on a new patch. However the devs have been careful to avoid any assurances that this will always be the case.

You should be fine. Some of the build pieces have changed a little - like the hearth. So, you may notice some cosmetic changes. If anyone used any funky build techniques - like floating wood iron beams - those parts of your builds will break when one of you goes near it.

The update process to your world does take quite a while so let it run "Don't Panic" it updates your world btw then your saves update as per your settings (edit: they are adjustable now)

One thing I did that was a blast is start a new island seed where I could build on the island I spawned on. Because I had already squeezed everything out of the game on my original seed without mods or admin, I just used free build to build out a cool base without exploring off the island. When the game is finished, I have an awesome base and an untainted world to conquer. Of course, I kept my "main" world for normal play. Great way to have a blast while waiting for the game to be finished!

So far yes.

They try to do that but make no promises.

Any explored areas will not be updated, only areas you have not been on the map.