Modal verb without auxiliary verb

I'm used to seeing modal verbs followed by auxiliary verbs, like this:

I should have been reading.

However, I've heard people say things like:

I'm glad you did or I wouldn't met you.

I knew we shouldn't trusted him.

Is this construction without the auxiliary informal?

Is there a difference if I rewrite those sentences as:

I'm glad you did or I wouldn't have met you.

I knew we shouldn't have trusted him.