When using the C-Stick, also make sure it's set to Tilt Attack in control settings, as Smash stick can cause similar aerial momtentum issues to inputting aerials via L-Stick + A. That's basically the jist of why you want to C-Stick aerial in most situations, because when using C-Stick set to Tilt stick (though some characters such as Peach/Daisy CAN benefit from Smash stick imo) you're conserving momentum in the air. This allows you to use the L-Stick to gain momentum to do things such as retreating aerials, or just lightly ease into the attack to microspace. For attacks such as UAir and DAir, using the C-Stick isn't nearly as important, but it's still preferable as it leaves your control stick free. So the big reason as to why you want to use the C-Stick (set to Tilt stick, that is) is both because you want to be able to conserve aerial momentum, AND so you have a free L-Stick to use as you need.
In terms of short hops, how you do it also matters. For example, the complex buffer system in Ult allows for a TON of things, one of these being 'fusion' attacks. These are the combination of jumps, specifically short hops, with attacks. They are the result of pressing a jump input AND an attack input at the same time. This will cause an automatic short hop, and it also forces the attack to start right as your 3 frame jump squat ends. The result of this are aerial attacks that ALWAYS come out during the peak of your jump, which might not always be what you want to be doing. Manually short hopping and THEN inputting an attack allows you to attack with an aerial as you fall, which with MANY aerial attacks allows you to cancel the moves animation and negate landing lag.. though not all moves have this ability and there's typically a window of when you have to time it to do it correctly. It varies greatly from character to character.
Wrapping up, being able to follow up on attacks for combos and such is a.. very fluid situation. It's not static by any means and can be influenced by MANY factors such as SDI/ASDI, where the hitbox connected (factoring in things such as sweet/sour spots on hitboxes), the percentage they were at, ruleset things that some people may change like launch rate, the weight of the character you're fighting, the fall speed of that character.. the same things on YOUR character also matter.. there's a ton of variables in play here.
The only real thing that's gonna make it easier is practice and experience. I recommend getting a human being to sit down in training mode with you and do NOTHING but DI / Jump / Dodge as you try to see what sort of combo options and follow ups you have at certain percentages. The shuffle feature in training is basically worthless, also make VERY sure to have move staling turned on as that's one of the many other factors I mentioned. Also, some characters in Ultimate have INSANE combo potential that can basically 0-death people.. while other characters have a smaller focus on combo game and say more of a focus on neutral game. So your choice of character and what attacks you go for, along with opponent percentage + weight / fall speed & then their DI.. I'd say of the MANY variables those matter the most by far. They are by no means the only variables, however.