1. Most of the times, I'm unable to recognize a solution with 7 or less moves. I mostly end up with 8, 9, or 10 moves solution.
2. My inspection sucks. I can't plan the whole cross in my head, and execute it blindfolded. I usually remember 2-3 edges and then look for the rest.
3. I'm still solving my cross on the top. Solving it on the bottom is so awkward and horribly slow. I tried to practice it but my time didn't improved.
Sorry for my poor English, not my native language.
Your English is fine, probably better than most people on forums these days. As for the cross, I'd say the biggest problem is 3. Sometimes even if it seems slow and awkward at first, you just have to stick with it for a while. Eventually it will get easier, but the longer you wait to switch, the harder it will be to do so. As for inspection and planning out the whole cross ahead of time, I still have trouble with that as well sometimes but again, you just have to keep forcing yourself to do it until it becomes easier. Also don't worry about the 15 second inspection time rules...take as long as you need to plan it out for now.
Finally, as far as 8, 9, or 10 move solutions, I'd say don't worry about that as much right now. Being bale to remember and perform a 9 move cross quickly and without pauses will still be faster than a 7 move cross where you have to stop and think about the last piece. Once you get the other parts down though and do want to work on reducing the move counts, I would say pay particularly close attention to the parts in Badmephisto's videos about the relative cross and about using the same move to solve one edge and at the same time convert another one from bad to good. Also just scramble the cube and play around with it for a bit trying to look at a few different options and see what ends up being the best way to solve the cross for it. Finally, if you get one you really can't figure out, use a program like cube explorer or Prisma Puzzle timer to show you what the optimal solutions are, then study how those solutions actually work.