Kapusta

Just use the middle ring position of the 3x crank you already have. Get a narrow-wide ring to replace the middle ring. You just need to know the BCD of your chainring.

8, 9, and 10 speed cassettes all use the same width freehub. So yes, a 10 speed cassette will work on your hub. Also, many 11 speed cassettes will fit as well (the shimano HG style with the 11t small cog)

You just need to decide on which 1x10 or 1x11 shifter/rd you want to go with. There are many to choose from. I did 1x11 conversions on two bikes using 3x cranks. One with Shimano SLX, shifter/RD, another with XT shifter/rd For both I used a Sunrace 11-46 11 speed cassette. Shimano Deore has a 1x10 shifter/RD and 11-46 cassette. Microshift also makes some good 1x9 and 1x10 systems (shifter, RD, cassette) with a really wide range. A buddy of mine just set up the 1x9 with a 11-46 cassette. Unless there is something weird about your bike, any of these should work for you.

If you want a sample parts list here is a 1x11 SLX setup that will probably work on your bike (though you should give all the specifics first) It is pretty much the same as what I used. This should be everything but a new cable/housing

Shifter: https://www.jensonusa.com/Shimano-SL...-Speed-Shifter
RD: https://www.jensonusa.com/Shimano-SL...ear-Derailleur
Cassette: https://www.jensonusa.com/Sunrace-CS...speed+cassette
Chain: https://www.jensonusa.com/SRAM-PC-X1-11-Speed-Chain
RIng (I am guessing at your BCD. Also, you could just try the ring you already have and see how it goes): https://www.jensonusa.com/Race-Face-...Wide-Chainring

You will need either shorter chainring bolts (since you don't have a big ring, but I think a simple bashguard looks cleaner:
https://bbgbashguard.com/ (you will need to know the tooth count of your single ring so the bash will cover it, and the BCD of the crank)