Wheelbuilding is a thing you get better at; most of us were not very good the first time.

Humans can (briefly) exert much more than 250W so any ordinary rim should be fine.
Eyelets are little rings that are crimped around the spoke holes to reinforce them; double-wall rims have double eyelets.
The spokes should be the correct length, so as not to extend past the nipples - and their ends are supposed to be covered by a rim-strip, which protects the tube from the nipple ends.
You will likely need new spokes - or at least spokes of the correct length (spokes can be re-used, but more than a mm or so away from the correct length is a problem).

Tubular tyres are sewn together at the base and glued on to a rim that has only a shallow curved surface. Clincher (properly called ("wired-on", even though some of them have a bead that isn't a wire) tyres need a seat on the inside of the rim; those with not-wire beads need a a rim that has a "hook" on the inside of the rim walls, to hold the bead in place.
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You could dis-assemble the wheels and remove the anodizing with a NaOH solution, and re-build them - that would save you the $75 or so you'll need for new spokes.