You should be able to use the graphics card. The power supply shouldn't be an issue as long as it's not proprietary, but it might be something to consider replacing if it's sufficently old (8+ years). I don't have personal experience on that, however.
Sale prices are down to OEM, seems everyone's past the whole crypto thing (and it's moreso other tokens; BTC mining hasn't been profitable for GPUs for a long while).
Any computer store should have OEM Windows 10 licenses; not sure how user licensing works these days. I know some licenses are bound to the Microsoft account, but I'm still on 7 myself.
Depends on your desired CPU. Intel and AMD are fairly competitive at this point; you'll have to decide on that yourself. Your current latest options are Intel's Coffee Lake (8th generation) and AMD's Ryzen and Threadripper options. I don't have any personal recommendations here since I don't own any of those; I'd be looking at the same benchmarks you would be.
Cases do usually have stock fans in my experience, but it varies (higher-end ones may forgo stock fans and have you buy them separately). Stock fans should be fine in most cases (i.e., not overclocking and indifferent about the noise level).
CPU coolers and thermal paste. Stock is generally fine for defaults, but similar to case fans, you might want to go non-default if you want better cooling / lower noise levels.
Desktop RAM prices are a bit higher than they used to be, and you do have to go for DDR4 for any builds with newer parts.
Logical Increments' recommendations are up to date with modern parts. It looks like Ryzen is solid for mid-range offerings. I used it back in 2012, but being a little wiser now I'd definitely recommend using it as a baseline and not a definitive source (that is, look for sales as well, rather than purchasing the recommendeds).
Similar to sales, you can also take a look at secondhand offerings.