Is it acceptable to submit more than one papers to a conference? I am an undergraduate and am new to paper writing.

I have been writing papers with professor A at another university since I was in high school. We are writing a paper together for an upcoming conference (which is pretty big).

I have been also writing a paper with professor B at my current institution for the same conference.

I am also writing papers with some graduate students for the same conference.

But - in total, I will be submitting about 5 different papers to the same conference (all with different people!). 

I don't know if this is acceptable in academia. That is, will there be any sort of consequences for submitting a lot of papers to the same conference?
Yes, it is acceptable, particularly since the author lists will all be different.  Go for it!  

One word of warning: The papers themselves must have clearly different content.  If you submit five nearly identical papers, the editors are likely to accept at most the best one and reject the rest.  That will annoy your other co-authors mightily.