[Legolas]

Being able to pause a multiplayer game is a server setting. DMs are always able to pause a module, players may or may not be.
As our bard said, if a lot of players use the pause button often that's plain annoying for the rest. For this reason, most servers disallow player pausing.

Exceptions are usually found in the Story or Campaign modules intended for a small party.

Saving the module in multiplayer stores player locations and the state of the world (monsters slain, items left behind, etc.). It won't spawn PCs when their player isn't there though. Saving, again, is limited to DMs only, and is most often used when players only have time to finish part of a module in any one session. Actually reloading because something was done incorrectly is rare.

What you can save is your character. This'll create a copy of the character with levels, items, and whatnot, and put it in your Local Vault folder, even in a Server Vault game.