Just as you stated, the cross needs some work. Your cross to F2L transition also needs a good bit of work. Your look ahead over all isn't that bad, but you had a 5-6s cross, so that definitely killed it. You finished F2L around 17ish (not too bad I suppose). Learn how to do the easy OLL cases from multiple angles to prevent the unnecessary AUFs (such as you AUF'd to lefty chameleon which would easily be done righty, although I often don't do the lefties when I should. If you don't want to do RH versions just learn other algorithms for the various angles). It took you a decent pause to finish that J and stop the timer, try to anticipate the end of the PLL and be ready to drop it and start the timer. PLL finishing AUF should be known before you even start the PLL, so as soon as you finish it you can AUF almost at the same time as while dropping the cube and your hands (it should be as quick as doing the U's in sexy move, and should flow like it was originally part of the PLL).
Your LL is not too bad really, 6-7s and that's using a 3LLL. Depending on my OLL/PLL case I average roughly the same. Take four seconds away from your cross, and you'll notice that your 16-17 F2L turns into 12-13, which with that same LL will turn into 18-20. Work on the first pair transition, that'll take off 1.5-2s, that knocks you down to around 16.5-18.5. Obviously the times will all vary, but if this was your average solve, this is what I'm basing it off of.
Everything toad says is right, especially the turn speed, but even still a 7s LL for not even sub20 yet really isn't bad.
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