Backcourt violation?
 

Team A throw-in from the side line. A1 catches the throw-in with one foot in the front court and one in the back court. Violation?

No, it's not. The player is in the BC. There's no rule against catching a throw-in pass in the BC.

Always Know Which Foot Is The Pivot Foot ...
 

Not yet. Remember there's no team control on a throwin. But, as an official, this is a violation begging to occur, so you have to be ready, and observant. If A1 starts pivoting, using the foot in the front court as the pivot foot, and moves the nonpivot foot from the backcourt, into the frontcourt, and then, back into the backcourt, then you have a backcourt violation. On the other hand, if A1 uses the backcourt foot as the pivot foot, then he is allowed to move the nonpivot foot from the frontcourt, into the backcourt, back and forth across the division line, with no violation occurring.

No, it is not a backcourt violation. Team A is allowed to throw it into the backcourt because there is no team control during a throw-in, and in the play, A1 has a backcourt location.

To add to this....

If A1 catches the pass with a foot on both sides of the division line, then pivots with his backcourt foot being his non-pivot, if he picks it up and puts it back down in the BC it is a violation. Once he picks up his BC foot, everything is considered in the FC.

Unnecessary and irrelevant: "from the sideline"
 

Team A throw-in would suffice. It doesn't matter where it came from. If that helps.