in the attached pic of the hose diagram, what would be symptoms if the blue hose that is circled in red poped off? How about if the Purple/pink had poped off? Basically im trying to get an understanding of what these hoses are for.

 

Those are the oil injectors for the engine. If there was no vacuum source for those, they would just drip more oil during shut down, causing some smoke at start up (as the engine would burn off the extra oil dripped from shut down).

It wouldn't cause an engine failure. Many single turbo guys don't resource ttheir vaccum source for those when they remove the stock twins (since they stock vacuum source is on the primary intake for the oil injectors).