Sims 3 expansion packs?

Yes. You can have all expansion packs installed and you will have access to all of the content from everything.

Yes. All content from all AddOn packs are constantly available and can be mixed as you please.

You're also able to visit all locations added in World Adventures when playing in the map introduced by Late Night

I recommend to you to install the expansions in the order in which they got released due to personal experience. The game sometimes refuses to rewrite files from newer expansions.
This shouldn't be a problem when you run it via Origin

Late Night got release after World Adventures. So Install World Adventures first when you don't run the game via Origin.