What happens when I use my titg while having a forgotten shoggoth in play?

1. both cards including any characters go to the bottom of the deck OR
2. character enter play insane and all other cards (support/event/conspiracy) go to the bottom of the deck?

I believe its nr. 2 because with titg the character never gets discarded INSTEAD they are put into play insane and the ability of the Forgotten shoggoth never takes place. Am i right?

That's how I understand it, Darkman. There is a check that must be made before cards are discarded. That check being whether or not it is a character.

So characters come into play insane while all other cards go to the bottom of the deck.

Precisely.