Shaun;
Cross
From looking at your solve it seems like you should actually solve the cross and first layer on the top considering your few mistakes when putting the corners in seemed to be because of the colour recognition which I believe is easier to see from the top... But if you like solving it on the bottom, just keep practicing and get better recognition with the colour scheme of the cube and try practicing the cross by scrambling --> trying to memorize as many cross pieces as possible when inspecting --> solve. Also try to get your move count when solving the cross to under 8 moves consistently

. When I first started my cross was pretty bad also but it got good really fast when I started considering lower move count > speed.
F2l/4Look last layer
If you decide to learn f2l be prepared for your times to go up dramaticlly for a while... I personally learned 2 look oll and pll before f2l which improved my time slightly, though even this took 2-3 days of practice before my times were equal to my beginner solves. I suggest just learning intuitive f2l first then move to oll/pll, but either way works ok. I find that f2l just takes more thinking, oll/pll more memorizing to start but easier once you feel comfortable with the algs. The problem with f2l is that it'll take a fair amount of time to get better at, it took me a week (on holidays) to get my averages down to the same as my beginner method (which was around 50 seconds at the time.) Though I think my main problem was that I cared about time at that stage so would rarely practice f2l, when I did improvement came quite quickly though

. Within the next week or two I got my averages down to sub 40 and since haven't cubed that much (the past two weeks.) But am still improving

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So yeah, the best way to improve is practice, get better at recognition (through practice) and practice more.

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Edit: I also don't believe lubing your cube is necessary for quite a while, it doesn't improve your times that much anyway in my opinion, though getting a speed cube probably will

. However if you do want to lube your cube, go with Lubix/Jigaloo/Crc silicone spray/maru lube etc... There's plenty of good lubes around, I personally just recently lubed my cube with crc because it's what I could find in stores.