It’s kind of difficult to relate the timing of a combo over a written forum post. First of all, I would hope that if you’re practicing this in training mode you have the dummy set to “Auto Block”, this way you can visually register whether or not you’re timing is too fast (the move doesn’t animate at all) or too slow (the move animated, but the dummy was able to block it). That’s the easiest way I’ve found to zero in on the timing of a particular combo, because ultimately you’re going to have to figure it out for yourself ( I mean I can tell you that linking low jab and low fierce is a two frame link, therefore you’re button press must register in at least 2/60ths of a second in order for it to combo. But how useful is that information to you in actual practice?), just play with the timing of the button presses until they start to combo together, eventually you’ll find that the timing has become muscle memory and you can do it consistently.
As far as canceling the uppercut, if you’re holding down, once you’ve registered the low fierce wiggle the stick from down, to down towards back to down and back to down towards and the uppercut should come out. That is a shortcut, however; you could input the full Shoryuken motion, but since you can get away with the shortcut in Street Fighter 4, why not?
I’m confused by your wording here. You don’t actually need to Plink this combo, since it’s a two frame link, though you certainly still can. In all likely hood your timing is off, and that is why the moves aren’t combo’ing. I would focus more on the timing of the button presses for now, don’t get too hung up on Plinking, Plinking is useful in this game but it’s only really useful for widening a 1/60th frame timing window to 2/60ths of a second, if you’re having issues with more generous link timings, it’s best to buckle down and get the timing correct, and than the one frame links can be plinked and your practice with the wider links will have come full circle. Basically what I’m saying is that you’ve jumped a few Street Fighter 4 lessons forward without establishing the foundation that would make those later lessons useful; build a foundation, than move on to advanced techniques: i.e. Plinking.