Do pending traffic violations and pending dui's show up on a background check

A criminal history check will show your arrest.

Yes, they will show up on a background check, even thought there is no resolution yet. Therefore, it is important to get the cases resolved with as little damage as possible. DUI arrests can have an adverse affect on your eligibility to drive, even well before your court date and regardless of whether or not you are eventually convicted. Therefore, I strongly advise you to go and see a DUI attorney for a consultation asap.