The Interpretation I was taught, by a now Football League referee, was any part of your body which you can gain an advantage from ( i.e use / score) so yes, if your arm was offside, but everything else wan't, I wouldn't be giving an offside decision.
Yes 100%. I wasn't at the game , but I know the situation you are talking about.
If, when the ball is kicked a player is in an offside position, and regardless of where he receives the ball from the pass, i.e in your own half, he is offiside.
Otherwise you could have players standing well...