first down

i believe the ref would mark the spot where forward progress stops.

so, no, he wouldn't lose the first down...

he would, however, lose his spot on the team right quick!

Yes. If a player crosses the first down line, then backs up of his own accord (not forced by tacklers) and is subsequently tackled, he will not be awarded the first down. If a player is running forward and is pushed back by the defense, he gets credit for forward progress.