1) When you release a Pokémon, the PokeBall is not obtained.
2) Yes. Dusk Balls work in Ultra Space, just like all PokeBalls. Do they get the increased capture rate in Ultra Space? Well, as long it is night time, it should probably work. Looking at the Bulbapedia Dusk Ball pages, and the Bulbapedia Ultra Space page, there was no information to prove otherwise. I'm not sure if it will get increased capture rate when you are in a cave in Ultra Space; yellow portal for example
One of the Rotom Powers. It increases the chance to catch Pokémon a lot.
Unfortunately, after looking at every article there is, there is no confirmed information on the exact effects of this Roto Loto power.
The Timer Ball is a PokéBall that works best on Pokémon as the duration of battle increases. If up to 10 turns have taken place, the Capture Rate is 1. If between 11 & 20 turns have taken place then the Capture Rate is 2. If between 21 & 30 turns have taken place then the Capture Rate is 3. Finally, if over 30 turns have taken place, the Capture Rate is 4.
As of Pokémon Sun & Moon, it runs off of a formula (1+.3*Turn Number), with the maximum being 4
The effects of Timer Ball first comes into effect during the 11th turn.
Yes. Paralyzed Pokémon are 1.5 times as easy to catch.
Of course, there is lots of information for these games that aren't confirmed. They are fairly new games, and it's difficult to find exact odds for some things.