I was arrested 25 days ago, three misdemeanor charges. I am waiting for a trial date. I have a new employer who is going to run a FBI/NCIC background check real soon. Will these charges show up?

Yes. Unless they are dismissed at the trial. It will show your arrest if you were processed booked etc.

Any criminal report will show the arrest, what you got arrested for etc.

They are running a check on you AFTER they hired you? That's unusual but you will likely not be terminated unless you lied to them about never being arrested. What type of work do you do for them, is the arrest related to your type of work.

Yeah in PA they do a statewide check, Im good, my arrest was in DE, But they also do a FBI/fingerprinting criminal check, the application asks was I ever convicted and which I wasn't and the arrest was 4 days after I completed the application.

Arrests don't show up to the public, only convictions.
So if it asked where you convicted, no you are not convicted yet, if it asked have you ever been arrested then you were.