Drop-shot is quite annoying, sometimes hard to master when trying to shoot, aim and go prone at the same time, however if you master it, you will be able to beat down many enemies when doing drop-shot. Sometimes doing drop-shot is not always successful.
Pre-fire is normally what you should do, if you sighted an enemy from afar, hide behind a obstacle/object, just fire your gun just when they're near the obstacle/object or near you (do it from the hip, don't aim - use the crosshairs to aim) which is useful to surprise and kill your enemy when jumping out of a obstacle/object.
Jumping while shooting - I guess I know what you mean, when your enemy is in close combat, and you aiming and firing at the enemy, you jump so they miss some bullets, leaving you to kill them quicker... well don't, if you jump when the enemy is close, the enemy would probably melee you instead.
Or the other case, you jump off from a height while shooting, well don't do this as well because you cannot aim effectively when falling from a height - which will also leave you some damage to yourself that you will be able to be killed quicker.
All you should do is have a good weapon and a secondary (I choose ASP dual) so when I'm reloading my primary weapon, I switch to my ASP dual, or I use the Ballastic Knife when in a small map so while reloading, I switch to the Ballastic knife and shoot a knife at them, or knife them instead.
It's all about how you play the game, less running, more kills - you are more likely to see enemies away from their team, because if you're running into a team, you'll be dead before you can aim or even shoot them.
Use the appropriate weapon, preferably your best weapon you can effectively kill enemies and choosing the right perks and equipment.