Wait wait wait… you’re having problems with s.HP into tatsu, but NOT having problems with tatsu into cr.HP? o_O I assume that you’re not able to do tatsu > cr.HP easily, since you say you are a complete noob, and THAT’S the part that’s a 1-frame link.
This might be a little long, but I think there are some conceptual things you’re mixed up on. I’ll try to clear them up.
“Linking” is stringing two moves together with pure timing, waiting for the animation of the first move to finish before inputting the second move. Doing, for example, a standing lp, followed by a ducking mk, is a link; you have to wait for the lp animation to finish and then hit mk with the correct timing to make them combo. Adding a crouching HP after the tatsu is another example of a link (and a rather hard one).
Doing s.HP into lk tatsu is a cancel. The tatsu begins before the HP is done animating, “canceling” the recovery of the HP and going straight into the tatsu. Such canceling is quite common and is the basis for chaining a special move after a normal move (not just in SF, but in many fighters). If you’re new to the concept, it might take some adjusting to, but I think that once you get used to it, you’ll will find it to be one of the easier parts of SF combos. You do your normal, then more or less immediately input the command for the special move. The timing isn’t as precise, you just have to be quick.
Plinking is a technique that really only applies to trying to perform *links, *as detailed above. It’s not necessary, and isn’t really applicable, for adding a special on the end of a normal. It you can’t get the special to come out, it probably is a matter of not doing the motion fast enough, or not doing it smoothly enough after doing the HP. Can you do the tatsu by itself consistenly? If so, then it’s basically a matter of practice. Aside from M3SS3NG3R’s suggestion, one other thing you could try would be crouching HP into tatsu. It’s not the combo you are trying to do, but it’s easier since you are starting from the down position, and it might help you to get used to the timing of canceling in general, to get a feel for how fast you need to input the special after the normal move. Once you are more comfortable with that, move back to standing HP into tatsu.
As for negative edge, it can be useful for specific combos (mainly when the same button is going to be used for the normal and the special, otherwise it doesn’t really do anything for you). And what you described in your first post doesn’t really sound like “plinking” per se, and again, plinking isn’t really applicable here. You just do the HP, then immediately do the motion for the special move (in this case, tatsu).
Hope that helps!
The timing of the button presses themselves is less important than doing the motion for the tatsu quickly after the HP. You do the tatsu motion and hit lk just as you finish the motion, just as you would if there were no preceeding HP. Basically, try to think of it this way: you’re doing an lk tatsu the same way you normally would. You’re just doing a st.HP beforehand. Also, one last note I didn’t think of before: note the difference between a close standing HP and a far standing HP. You must be within the range for the CLOSE version to come out; the far one cannot be cancelled into specials. And to do the full combo you laid out (st.HP into tatsu into cr.HP into EX tatsu), that first HP needs to be at point blank.