you NEED THAT ARM. its holds the internal brake member stationary on the axle. remove it and one day it will loosen off and either destroy the wheel bearings and seize, you will crash and die, or go all wobbly, destroy the bearings, collapse, and you will crash and die. been there, done that!
at some point the pedals jam and spit you off as it unexpectedly becomes a "fixie"...
there is enough space to get the sprocket behind the arm. you may have to bend it slightly. use low profile head bolts... etc. think a bit
but you need that arm, and it needs to be secured to the frame!
for a rim...scrapyard, backyard, shop, ebay...anything. count spokes. 36 is standard. you want to find an intact rim that has a hub close to the same size, within a few mm where the spokes mount! look at how its "laced". there are various combinations, radial, cross two, three or four... you will need to copy the existing pattern or find other spokes of the correct length. cross four (even more!) is strongest. radial is weakest.
there are spoke calculators online, i find its easier and cheaper to stick with what you can find though. spokes alone are about $3 each from a shop here, without the nipple! hence why you match things as close as possible.
online. if youve never attempted to lace a wheel...theres heaps and heaps of literature, and only practise makes perfect! after a few, you can do em in less than an hour...