Yes I have a tip for you F2L. Don't look up algs. Just practice it and try to understand how the pieces are put together, it is usually not that hard. Either the pieces are separated with say, a corner in a slot. Most of the time you can take it on the top layer and pair it with the edge at the same time. Other cases are a little less straight forward but you'll get them. Other common cases are the ones where the pieces are already together, but not oriented correctly, for these most of the time it consists of separating them and putting them back together the correct way, or coming back to the basic case where you have two different colors on the U face of your pair cubies and solving it with RUR' and such. Inconsistent progress is going to follow you all the way down. There are days I can average more or less 30sec, other days I am at 35, and I heard many people more or less sub20 saying this too.
About your cross, go on youtube and check badmephisto advanced cross video. What I did until about sub50 was aligning each corner edge with its face. So the blue/white ( white cross ), would be aligned so that the blue side of the edge matches the blue center of the blue face, and then I would just need to rotate it to get it down and solve the piece. What I do now, I put every corner edge on the bottom face with white on bottom so that. The only restriction is to keep the order of the edges which is a little confusing at first. You already know opposite colors I suppose, so orange opposite red and green opposite blue. And then if you remember the WCA orientation which is white on top, green on front, orange on left and red on right, you can easily remember the order once you white cross is on bottom. You just invert it, meaning orange goes to right and red to left. Also, avoid cube rotations during cross, even if you have to do a B or F move. Cross is usually not that much about tps since you can get it under 6-7 moves most of the time. Also, worst cases are the ones where you have an edge on the top layer which is inverted, meaning a R2 F2 L2 or B2 is not going to solve it. For these, the best is to use the turn of another face to orient it. Take a solved cube and perform : R F' U'. The cross is solved except two pieces. You see that if you perform an F move you're going to solve one more edge, but it'll leave you with an incorrectly oriented edge on the top layer which you absolutely wanna avoid. Therefore to solve it the most efficiently, the idea is to use this F move to orient the edge on the top layer. So you want to bring this edge on the front face to benefit from this F move that you'll have to perform anyway. So the good way to solve the case would be to do U F R'. And a last thing, try to plan as many moves as you can for the cross, even if inspection takes a minute or more. While doing slow solves you can count how many moves you perform to solve the cross. If it's more than 10-11 it's definitely bad, if its in the range 8-10 and you feel comfortable with the moves I guess it's ok ( I myself sometimes end up with 12 moves but I use one or two triggers such as R'uR'u' ( changes the orientation of the edge on RD ). So if I see that I can do a quick cross but would eventually end up with an incorrectly oriented edge on the R or L face, I use this trigger which is really fast to perform ( left version is : Lu'Lu ). This is in badmephisto's video along with other good tips.
Also, obviously you've been through a lot of things to improve lately, 4LLL, F2L, they all take some time to improve. But keep doing full solves for now, the more you go on, the more you'll understand about how pieces move, you'll find shortcuts for cross and F2L, you'll get better at drilling algs and recognizing F2L / LL cases. I bet at the moment you have a lot of unsure moves and pauses that your timer does not forget. So, until you're sub60 or sub50 I wouldn't worry too much, it'll happen so fast that you'll soon be asking about how to get sub40.
I got a sub4 cross at 32sec average, so I believe with your times your cross must be at least sub3 by now !
Edit:
Also, one more reason not to go for F2L algs : most of the time they assume the only empty slot you have is the one that you'll solve. This would be the worst case, meaning you'll drill an alg that is longer that what you could solve in 75% of the cases ( since 75% of the F2L pairs you solve are done with 2 or more empty slots ). So, knowing that you have additional empty slots gives you additional freedom to hide corners or edges. What I do to practice F2L at the moment is taking a case, and try to reproduce it, then solve it. All intuitively of course, and I repeat it until it is in muscle memory. What makes it especially hard to learn is that there is a huge amount of cases than can happen ( actually much more than the 41 ( +1 solved case ), since you can also have all these cases with empty slots, and for each case you should be able to solve it in the 4 slots ( so it's 4x41 at least, even though there are lots and lots of mirrors ). The idea on the long run, is to have them all in muscle memory so that when you find your two pieces, you can execute the moves while "looking ahead", which can only happen once you're really confident at solving F2L pairs from every angle.
Sub-15 average shouldn't be a problem.
