Go SS specific with the sprocket, they last a lot longer and are far more tolerant of the chain bouncing around. Cassette sprockets are designed to chuck the chain off the moment it goes out of alignment (i.e. the mech moves), so has the potential to do that when the bikes bouncing around too.
Front chainring will be fine, if a bit expensive to wear out a nice one for no reason.
3/32 SS chain is far stiffer than 10s/11s chain, it won’t twist and jump around and get itself pulled off the sprocket.
You might get away with 11s chain and an old sprocket just to give it a go, but it’s not perfect. Especially with a new chain on an old sprocket which can slip if the sprocket isn’t in perfect condition still.
KMC Z610 is the dogs bollocks of SS chain and costs <£10
On-One Groove armada sprockets are £13 at the moment.
After a lot of trial and error I’ve found the single armed tensioners to be just fine, if the chain comes off it’s always been something else’s fault (they still put a lot more chain wrap on the sprocket than a rear mech). The only thing better is a proper SS frame, a setup worn enough to jump the sprocket on a tensioned setup will last hundreds/thousands of miles longer on a proper frame (you can go until there’s barely and teeth left on the sprocket!)