I agree with your tips, but what I would add is that it is very difficult for you to be VERY GOOD at several games, the best thing to do is to dedicate yourself to just 1 game, and when you are VERY GOOD at that game, we will certainly The next FPS you play will have a much better sense of aim and recoil than most players.
So always focus on playing just 1 game, and become good at it.
my personal non general kinda tips for improving your aim in a game like league of legends:
1#focus enemy legs
2#when aiming put your mouse on their legs and when shooting the skill shot make sure that u also look at where the enemy is looking as sometimes he might juke u and u end up wasting ur ability and sometimes mana
3#make sure u keep the enemy in ur spell range like its that obvious
4#always fire ur skillshot when u are sure the enemy will at some point in time be in the area u are shooting ur skill shot. such as a wall beside the enemy or when the enemy is csing.
after all the more pracitce u do on the tips i mentioned above in game should easily make u a irl sniper. also for beignners try to focus on landing ur lux E's and Q's.
if you are not hitting the shots like u used to before, dont change the sens or your settings, its just a bad day, the way you were shooting the other day, is not gonna be the same like u are today, just warmup a bit, but find a nice sens that fits you before anything