Can the food in the steamer be heated quickly and evenly?

I wouldn't say "quickly" per se. I've only steamed frozen dumplings so far and takes about a good 15-20 mins depending on your stove heat. I'd imagine non-frozen foods will steam much faster.

Do steamer racks and pans rust easily?

I have had mine for a few months I use it a lot and put it in the dishwasher, so far no rust at all.

Can you cook with this in a traditional oven?

Because its handles are made of solid wood, it doesn't fit in a traditional oven.

Is the handle of this saucepan solid wood?

I honestly can't tell (it DOES say "solid wood" in the desc). It LOOKS like wood (grain pattern), FEELS like wood ("soft" - not metallic - texture) but it could just be skillfully-done manufactured. The only way I might tell is to gouge it, but I just bot it, so I won't. It DOES keeps the handle cool even as you boil water, etc., offers a good grip, and looks good. The whole saucepan is functional (and cute).