1. Does the Vault 111 jumpsuit on the table respawn?

2. Can Vault 111 jumpsuits be pickpocketed off the deceased npcs there?

3. Are there other jumpsuits beside Vault 111 and 114 that you can obtain?

1. Not sure which table you mean.

2. No.

3. Yes.

Their is one in the vault where you find Nick Valentine, one in the vault you come from, and a lot of them in the vault that is to the west of dimind city, go west till you see a gear shape on your mini map. They have them for sale and you can loot them if you shoot them.
You need either 3 fusion cores to trade them or pass a speech check to get into the vault.

Actualy there is plenty more and a lot of them respawn as well so there is kinda limitless supply of them.

When you regain control of your character in Vault 111, there is a second room of the cryo freezers with two tables just by the door with a few coffee cups and a spare sealed Vault 111 jumpsuit on one of the tables

Did you check eveything in there, I checked eveywhere in 111 so there were no items left behind except the cryo gun behind the Master locked case