No tag after catch

[ozzy6900]

Playing OBR 16U Fall ball.
1 out - R3 & R2 2 umpire system.
Fly Ball to left, trouble ball near the line.

R3 holding on 3rd for the catch, R2 half way to 3rd. PU calls the catch, R3 takes off for home and is not played on. R2 heads for 3rd (never tagged up). R2 slides under F5's tag and is called safe by the BU. Lots of screaming and yelling that the R2 never tagged up. Finally F3 screams to F5 to throw the ball to 2nd. F4 receives the ball and says to BU "runner didn't tag up". BU now calls R2 out.

First question: Was this the correct procedure for BU (to call the play @3rd then wait for the appeal @2nd)?

Second question: if R2 was tagged out @3rd (now 2 outs) could the appeal still be made @2nd for the third out?