First on the mechanics question, you should stand with your arms at your side. It looks more professional.
As for the player into the net because of momentum, for NFHS rules, it is a net fault. In other rule sets, it depends if the result causes interference with the other team playing the ball --i.e. if the other player backs off because of the incursion into the net and this causes the ball to hit the floor, it is probably interference caused by the net incursion.
For the screen, if the ball is hard hit over the player --i.e. on a direct line, it is screening. If the ball was looped over the net, it may not be screening. Also, if the receiving team can shift to see the serve, it is not screening.
On the third question, you should wait until the ball strikes the floor or another player. This is because you can get a fault on the receiving team before the ball becomes dead that would counter the bad serve.
Hope this helps.
