His s.HK wont hit you while crouching, dont mater what. Plus that you can throw c.mp and it will beat the s.HK clean every single time, from any distance. You can hitconfirm with hadokens but it will almost never connect (you will be doing c.mp from outside Hawk’s c.MK range), he will have to block, tough. his EX Condor Spire will go trough the projectile but wont hit you (watch out for SPDs here, if he dont hit you, you have the oportunity to start a combo). If you hit confirm with HP super it will aways to connect.
He will keep mixing s.HK, c.MK and dashs into SPD. Sweep his c.mk, its reeealy easy, and once you will be crouching the s.HK wont hit you aswell (plus that the s.HK itself can be sweeped aswell). Take care about the dashs into SPD, you must be fast and stuff him with c.lp/c.mp and deliver a combo, I think its better than to jump back because you can get DPed or U2ed if he is playing loose.
Your c.MP will win or trade against his Ex condor Spire if you are just outside his c.mk’s range. Its hard to do that on reaction, tough. You can spam them randonly because at such range nothing he may to try will hit you. The Ex Condor Spire is punished by 3f moves (c.lp, dp) if it hits you early, but its safe if hits you at the end of the move, so watch out for SPDs in such case.
Its aways better to crouch block the regulars and EX Condor Dives, makes it easier to punish, if you think it can crossup just stand up and problem solved ( it can crossup a standing opponent aswell, but he have to go for it, once you are crouch blocking everything, he will try to do a CD that crossups a crouching opponent, but such CD wont hit a standing one so just stand up when you see it comming, then punish with hadoken/super/ultra)
If you block his regulars Condor Dives while crouching, you can punish him with hadokens and ultras, and if he aims at your head/shoulders you can even Solar Plexus him (dont try c.HP after it untill you get really used to that situation, it misses a lot due the distance).
The Ex Condor Dives will be punished by an U1 IF he hits a crouching Ryu on its head or shoulders, otherwise he will be able to block a reversal Ultra, and if he have meter he can Ex Condor Spire trough it and rape your ass. HP Super will aways punish it. You also can to step ahead when you see him EX CDing, so he will hit Ryu in a bad way and will get punished. It can end up giving him a crossup CD, but only if he aimed at your head, and good T.Hawks wont do that, unless they expect you to step ahead. Have fun with the mind game and remember, if you think it can cross you up, just stand up.
If the Condor Dives misses and land at point blank, you better be with your reaction up to date otherwise its gonna be a mind game that is in his favor. If the CD misses, just punish, the best one damage wise and meterless is c.mp, c.hp xx hk tatsu.
Theres a situation, that is very hard to happen but when it happens its dangerous. If the CD or the ex CD hits you in its last active frames (really near the ground) you will block it but Hawk wont jump back, he will just land as if it have missed you AND he will land safely, your 3f moves will get blocked (some people say his super is 2f, the wiki says its 1+2, anyway it dont hit Hawk aswell). Good luck guessing correctly here. Anyway its really hard to happen (and because of that its even harder to react to it, you never expect it).
About his ambiguous j. d.HP, its all about timming so I cant help you to dp or block it better, it depends on when Hawk jumps and when he pushes the buttom (if youre going for a dp trade into ultra, use the HP dp because you will have more time to throw the ultra after it). What I can say to you is that I tried to do 4 hit combos with the crossup j.d.HP and didnt managed to. So if you block the jump in and he did a standing anything, you can start thinking about to jump/backdash/mash something. Hawk’s frametraps aint that good aswell, he needs to be really close in order to hitconfirm a LP into a MP xx dp. Its really easy to see when he does j.d.HP, LP, walk in LP, cl.MP xx dp. He have to walk a lot in order to the cl.MP to connect.