To add a few more points to the good advice sneaklyfox gave:
For the cross you want to know your color scheme inside and out. I always start with a white cross (which isn't really something you want to do, if possible learn to be color neutral, or at least be able to start on opposite colors), so that means that blue is always to the left of red, and green is always to the right. You want to have the whole cross planned out during inspection (heck, that is something I need to work on). When you practice the cross, feel free to make your inspection as long as you need, because it will come down to the 15 second limit the more you work on it. Try to solve it blind after you've planned the whole cross.
Full PLL should help you a lot, or at least it helped me.
When gauging your f2l times, you want to include the cross, because of the transition between cross and f2l. Also, you'll want to use a larger sample size that just one solve, at least an average of 12.
4:15 "oh god." These are the moments that practice will get rid of. Those "oh god" moments when you just can't find the next pair
4:48 you say "no improvement whatsoever" but your slow time was 5 seconds faster than your fast time. Just sayin'
7:13 you say that going slower makes your times worse, and you don't understand because people tell you going slow is better. You are not supposed to have faster times when starting out slow solving. The whole point is to train your mind to fluidly move without pauses, it is a practice-to-get-faster-later method, not a getfastquick method. That is why I originally suggested not using a timer. Also, it is not just about "turning slow," but more about "turning without pauses." The reason you have to turn slow, is because you need to be able to think about your next moves to turn without pauses.
10:00 you are not a bad cuber, lol. Everyone can use more practice. I understand though, I too get frustrated when I get solves that are slower than my "threshold time."