sure looks stainless to me. Awfully shiny for carbon steel.

Usually the cheapest hand hammered POS will be your best bet.

Any of the carbon steel woks your links point to will be fine.

Get a round bottomed one. Flat bottoms are worthless-- might as well just
get a big sautee pan. You can't flip and toss the food right in a flat
bottom wok, and the flat bottom means that the intense heat that's meant to
be at the very nadir of the wok ain't so intense and is spread out all over.