Correct Switch?
 

C is opposite the table and calls an Illegal Screen in the front court on A1. The ball will be inbounds opposite the table.

After reporting the foul, does C go table side at the C or will s/he become the new L?

The way I read the manual it seems that the C will become the new L.

Incorrect term.

This is a switch, not a rotation. Rotations occur when the ball is in play. ;)

Also, you asked if the C will STAY tableside, but you said he was opposite table when he called the foul.

I will correct my original post.

Should be C or T depending on where the foul occurred. In Ohio, you would go back across.

I've never studied all the nuances of NFHS switches, but I'm pretty sure in this situation the calling official would stay opposite and become new Lead.

Correct (at least in most areas).

Treat it just as if C had called a travel or OOB instead of a foul.

Old L comes over and bumps old-C down the court to become the new L.

When C/T opposite calls a foul going the other way with no free throws, you don’t go tableside in any mechanics set.