You need more space above the CPU fan for sure. You should really try to get more than 8mm room cause even then it's a little cramped, but if that's all you can do then I guess ya gotta work with what ya got.
Also the retail heatsinks come with a thermal pad on the bottom as you've read, you DO NOT put thermal compound over that.
If you want you can remove that little bad using a plastic edge, credit card, something along those lines to scrape it off. You don't want to use metal because you don't want to scratch the heatsinks finish. If you can successfully get that pad off nice and clean THEN you can apply some thermal compound and you'll get possibly better temps.
Make sure you only put a little bit of compound on the CPU core, a very thin layer. You don't put the compound on both the CPU Core and heatsink as that will just be too much.
Don't know if there are 'standard fan screws' ya just gotta find some that'll fit. I have nuts and bolts on some of my fans. Also they have self-tapping screws which are usually what fans use. They go in without requiring a bolt or sticking out so it looks cleaner.