1 & 2) The cooler should fit the case just fine. I'm not sure it will really allow OCing however. The 7700 runs a bit toasty, but you'll be fine with the setup you listed at stock.
3) The PSU is older, but it's ok for that system. Due to the chip and cooler you won't be OCing anyways so you should be good to use that PSU.
4) Different pastes like these can make a difference of maybe 5C or so, but your technique will matter more. If the cooler comes with TIM just use it. AS5 is good, but aged by now. The cooler comes with good stuff, so don't worry about buying better.
5) You are going to ask which is better between a B250 and a Z270? Really?