Not all the questcocoons where shown, but all the ones that were seen were round.

No, All Jacks are from Derse.

The vast glub killed all trolls that did not have fuchsia blood. All the post-scratch trolls except Sollux survived because they were in the Medium, which is kind of a different universe.

They have cocoons because trolls are kind of an insect-based species.  And they have the slime to prevent them from having super terrible nightmares.

612 hours

Synchronize: Dirk leaves Sawtooth at his place to finish entering then flies to Roxy’s house with Squarewave.  He kisses Roxy so her dreamself wakes up. He teleports a bucket back in time.  Then he decapitates himself sending his head to an unconscious Jake, leaving Squarewave to bring Roxy’s house into the medium.

Between the two flashes Jake wakes up and talks to Lil’ Hal about kissing Dirk’s severed head which he ends up doing waking up Dirk’s dreamself.

Unite: Dirk and Roxy’s dreamselves are now awake on a flaming Derse with Jane’s dead body. Dirk kisses Jane so her dreamself wakes up. Jane then wakes up on Prospit and goes through a teleporter that takes her to the frog temple on Jake’s island.  Dirk and Roxy fly to the frog temple in the Medium and enter the lotus time capsule that sends them back in time where they exit on the frog temple on Jake’s island.  They grab Jane and fly to where the bucket that Dirk sent back in time and then go to where Jake is unconscious.  Dirk then takes the bucket dumps water on Jake so he wakes up and is able to kiss Dirk’s severed head allowing the whole flash to happen.  Then they all enter the medium from Jake’s house. 

http://www.mspaintadventures.com/?s=6&p=004064

If he did it didn’t happen in the comic

Yes

Aradia’s dreamself had always been on her questcocoon in the center of Derse.  So when Bec Noir was destroying Derse he killed Aradia’s dreamself and since she was on her questcocoon she ascended to God Tier