Speed is everything. In a fighting game, time is dealt with on a much smaller scale than most things. For example, Moonsong (Ice Arrow) is -37 frames on block, meaning that you have a little over half a second to hit your opponent after blocking it (which in fighting game terms is actually quite a long time). Your 5C starts up in 10 frames, meaning that you have roughly 27 frames, or a tiny bit less than half a second, to move around and react. Were you to use a faster move (let's just say 5B), you would have 30 frames instead since it has 7 frames of startup.
Now, when it comes to punishing Jin's DPs, there are big differences between them all. If you end up blocking the A or B version in the air using barrier block, nine times out of ten you can kiss punishing him goodbye since A is -17 and B is -11. C version is -40 frames on block, so you have quite a long time (relatively) to punish him. D version is tricky because of the second hit gaining unblockable properties when fully charged, being air unblockable without barrier, and being able to be released at any moment, but if you end up blocking the second hit you have 26 frames to hit him, so it's rather punishable.
If you're having trouble with those, try to practice doing a quick dash into 5C. 66 (return to neutral) C as fast as you can. You'll carry your dashing momentum if you cancel your dash into an attack, allowing you to start up your attack early and still make it within range to hit the opponent because you slide along the ground a short distance.
When it comes to getting out of pressure, the most you can do is wait for an opponent to leave a hole in his blockstrings and either backdash out, jump out while blocking, wait for the opponent to attempt to reset pressure by leaving a small hole while they recover from the previous attack (ala 2AAA dash 2AAAA), or use a reversal to hit your opponent out of their move. If you're going to attempt to reversal, it is a good idea to practice instant blocking basic pressure strings so that you can open up a hole in their pressure to take advantage of. You will pretty much never win by just trying to mash out of pressure with your fastest attack.
Important note: Everyone's pressure is different. You will have to learn each character's holes individually as you go. Some are more obvious than others.
As for not knowing what to do after you hit the opponent, I have three words. Practice, practice, practice. Look up what your options are after landing a specific move. The combo thread is always a great place to find followups for your combo starter. Once you've found something that will work, go into training mode and work until you can get it right. Doing it on reaction is a matter of experience fighting an actual opponent. You have to be able to make a judgment regarding whether or not the attack you use is going to hit.
Keep at it and don't hesitate to ask to elaborate on a point of two if I got a little confusing.