If you're going to practice DO NOT practice against the CPU, it will give you bad habits and it will be really frustrating because they have crazy reaction time.
Practice against someone who is at your skill level or better.
I don't get what you mean by jump mechanic, all you do is press up, lol. If you want to win an "air battle" just make sure you keep your eyes on who you're fighting against and be ready to press kick since jumping punch is useless.
Don't jump-in a lot since it's bad in any game, you will get uppercutt'd/roundhouse'd a lot if you do that too many times.
There really is no good counter for sweeps other than block low or jump and attempt to punish.
Mix-ups don't come into play in this game since there's no dash or run button and the high low attacks are too slow that by the time you attempt to do tricky stuff your opponent will be blocking.
Who ever your main is make sure you get to know how their specials work and how to use them in an effective way. It does a lot of damage and it looks cool too.
A good example is J.Cage ...
Nut punch -> (close) LK -> Shadow kick
You can always try to trick your opponent, but it's hard to do it in this type of gameplay.
Another example is J.Cage
Purposefully whiff shadow kick into a throw.
What I do most of the time is study the opponent in the 1st round and by the end of the round you'll notice how they play. Then you wait, punish, and go in the offensive or stay defensive in the next round.
Nothing more I can say other than you'll eventually get the hang of it yourself soon enough.