Modern digital transponders don't require you to set standby when changing code. When the last digit of the new code is entered it is activated; there is no "crossover" as you would get changing individual digits on an old style transponder.
> Also, if mode "C" is ALT, is mode "A" ON?
Correct.
S stands for selective. You're probably best putting Mode S into google if you want a decent explanation. No difference in the way you physically use it and no particular benefit for pilots. You will however find that not carrying a Mode S transponder becomes more and more limiting in terms of where you can and can't fly.