I am a Chun player, so I’ll see what I can add to this:
Crouching MP is a fantastic anti-air against Shoto characters like Ryu, Ken, Akuma, and a handful of other cast members as well. If you learn the timing for it, it can really frustrate some players with how good it is at keeping them out. Standing MK works as well but sometimes can trade.
I don’t recommend dashing forward after focus absorbing a jump-in, and here is my simplest explanation without getting into frame data or anything: when you are dashing, you can’t do anything, and in the time during your dash, your opponent has already landed and is capable of doing something, plus since you dashed forward you are getting closer to them. That’s a lot of things you don’t want.
As for punishing Shoryuken, don’t bother with the focus attack, just do a bread and butter cr.LK > cr.LK > EX Legs. Your choice for punishment might change over time as you learn more combos and your execution gets better, but for now I think that’s the most reliable punisher for you.
If you don’t have meter or want to broaden your horizons, cr.HP xx MK SBK can be a good choice if you’re close enough. Cr.LP > cr.LP (>cr.LP) > f.HP is a good meterless combo but requires good execution. Cr.HP xx HK Legs xx MK Legs is also a great combo but also requires pretty good execution.
The Focus Attack is also not necessarily for setting up Ultras - in fact, it’s generally a pretty poor way to setup an Ultra because the game scales down damage more heavily if you are combo’ing off a Focus Attack.
The Focus Attack is a great way to change the momentum of the game. It absorbs a hit (except armor-breaks and throws), which still adds to your Ultra meter, plus it allows you to slowly regenerate the damage you take from the attack you just absorbed. Use it to absorb fireballs and other attacks with long recovery like sweeps.
If you start charging your Focus Attack within Sweep range of your opponent (but out of range for them to do much else) you can apply pressure to them. They have to do something, because if they don’t, you can fully charge to Level 3 and crumple them. For example, if they keep walking forward, try to hit them with it and then backdash out of it - this will leave you safe if it was blocked, but still give you time to hit them with something else if it hit.
It’s very situational, and a lot of people do different things when you start charging Focus in front of them. The main thing to keep in mind is to remember what they did, and if you start noticing a pattern, figure out what you can do to punish them for it.