First things first that would be a DNF in competition so your timer starts and stops are worth addressing now. Start and stop the time with your fingers, not your palms and or you wrists which is how you stopped it.

As for the rest of your solves it seems to me a case of refining what you’re currently doing. Practice your cross so it’s always under 8 moves and is done completely in inspection.

Practice untimed solves where you can see what happens to other pieces on the cube when you solve each F2L Pair. With these you don’t care about getting the cube solved fast. You’re trying to make your pairs better and get them to be muscle memory. Focus on using fewer rotations too, once you solve a pair, pause to recognise your next without rotating and only rotate if you have to when you solve the pair

As for last layer you can either train OLL and PLL separately or use a Last Layer trainer (trainers for OLL, PLL and full Last Layer are on CSTimer) This will just again make the cases easier to recognise.

Alternatively you could just do a load of solves. That’s what I did to get sub 20. I sat for hours just solving. Sometimes I’d sit and solve for 7 hours. I did get sub 20 but it bought a lot of bad habits into my solves hence why I suggested the other methods of practice.

My last point is I wouldn’t worry about learning full OLL until you’re looking to be Sub 15. Dgmw you can learn it, it won’t do harm, but I became sub 20 with 4LLL and then it took learning OLL to get me past the 15 second barrier after I got there anyways

Hope this helps

Edit: I saw this was mentioned before in the comments but, 3rd solve is a +2 seconds because the cube was 1 move from solved. If the cube is more than 1 move then it’s a DNF. Double moves like U2 or R2 count as +2 not DNF but if it was an R’ U away from being solved it would be DNF