You can certainly request informal discovery, but the first thing I'd do is look at the NOTA (the ticket) and see if you can see any indication there. Sometimes there are tell tales.
The fact that there's a downward slope doesn't justify going faster.
After a TBD loss, you request a TRIAL DE NOVO. It will result in a trial date being set. There's no "arraignment" in this case. You've already are considered as having pleaded not guilty.

