Make sure it’s tight, road cassettes tend not to have alloy carriers as they’r esmall, so they can gouge freehubs
Nope, same as the MTB ones, only the cheapest don’t have a carrier.
As above you will need the 1mm spacer that comes with road cassettes to get it to fit on a 9s/10s MTB freehub, It’ll still index, but might need tweeking slightly to get it wo work properly at the low end.
You might be better off just getting a 10s MTB cassette and binning the big gears and usig a singlespeed kit to space the cassette out. IME the narrow gaps on a road cassette were really irritating downhill as you had to constantly search for a gear, or coast because it wasn’t worth changing 4 gears between corners.