Ineligible Downfield/Illegal Touching?
 

A81 lined up in the slot and is supposed to be either on the line with A82 off the line outside him or lined up off the line with A82 on the line of scrimmage outside him. Either way they are both on the LOS and A81 is covered. Ball is snapped and A81 goes out for a pass and
a) A16(qb) throws a legal forward pass that crosses the neutral zone to A9 on the opposite side of the field. Or
b) A16(qb) throws a legal forward pass that crosses the neutral zone to A81, who catches the pass and runs for a TD.

The answers below are what I believe is correct, but I'm not sure if b) is correct.
a) Ineligible receiver downfield by A81, penalty is 5yds from previous spot.
b)Illegal Touching by A81, penalty is 5yds and loss of down from the Basic Spot which on a loose ball play is the previous spot.

Please let me know if I'm thinking correct on this or not.

Correct for both.