There are two Coral ward quizes: one before and one after restoration. All the rest are post-restoration.
The Wedding Ring, Spoink Ball, and Randal are all connected. You don't have to talk to either NPC first, just start exploring the underwater City in the lake. First solve the Ring problem, then it segways to the Spoink quest. Randle's quest continues after the Spoink one; go back to Jasper ward and look around.
The mulch is started with the old man in a Peridot Ward park.
Talk to the gang leader in 7th street to start the job applications.
Go to Spyce to start the Grocery.
For Corrin-Rouge (ep 16 part), talk to the Jasper Police Chief. The whole quest starts back in the Grand Hall at the start of the game.
For Silph-Scope, go to Beryl ward and the forest to the left until you encounter Kelcleon. Then go to the Silph Building in Obsidia.
The Tara quest depends on if you talked to Simon back during the failed Metor attack on the Cabin. If not, you can't do start this quest. It starts by talking to Simon in Beryl Cemetary (can be done prior to restoration)