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That looks like a cassette hub, take the cogs out and if the body is like pic related (37ish mm long, notches end a bit before the edge, sorry about bad pic my camera is shit) you're set. If it's shorter it's a 7-speed or under freehub, if the notches go all the way it only fits 13t and larger smallest cog but you can use a 2-3mm spacer to fit cassettes with a 11t and it should be ok.
You can use 1x with whatever the fuck you want on the rear, the only things that matter is how much you want to compromise in range vs gaps, what your derailleur can handle in terms of cassette size and chain wrap, and how much chain retention you need. There's even 1x8 full meme groupsets now so don't think it needs to be that fancy.
