Outside of the already remarked upon versatility -- a wok makes it easy to do two types of cooking which aren't easily done in a frying pan. Together they're known as "ch'au." Separately they're liu and pao.
You're familiar with the word ch'au as "chow." As in chow mein. Which is really ch'au mien or wok fried noodles. liu means "stir," by the way. You're also familiar with the word pao, as in "kung pao chicken." "Pao" means "toss." Things chowed are liu, "stir fried," which means they're slowly moved around the wok at medium high temperatures. Things pao are cooked at very high heat and tossed frequently.
A wok allows you to use a little bit of oil in ways that make it seem like a lot. For instance, using a wok, you can pan fry in as little oil as you'd use to saute in a frying pan.
No. In the same way almost any sharp knife can perform almost any cutting task. You can make up for a shortfall in pan shape by combining an understanding of how you're trying to cook with the technique to do it.
That said, the best woks are very inexpensive, relatively thin, carbon steel. Don't buy an All-Clad, don't buy a non-stick, buy cheeeeeeeeeeep.
Pao and liu. If you're serious about preparing good quality Asian food, a wok or two will make a big difference. If you're wondering about cross-over purposes, a work makes an excellent and thrifty deep and pan fryer. Because there's a lot of agitation in wokking and sauteing, you'd thin a wok would make an excellent saute pan, but it's a bad choice for sauteing because when you saute you want to use the surface of the pan (contact conduction) but in a wok you want to use the heat of the oil (immersion conduction). As a substitute for a saucier, the shape isn't bad for quick reductions, but doesn't lend itself to the other aspects of sauce making like whisking. Also, most good woks are carbon steel and you don't really want to load them up with a lot of liquid which would screw up the season.
Just to clear up a misconception -- Pushing food up the side of the pan to hold, while cooking something else in the bottom isn't something that's actually done very much. Not that it's never done; and not that some of the best people don't do it often; just that it's more a "technique" described in an infomercial for hand-hammered woks which ran a while ago.
Evem more than western style cooking, Asian cooking is all prep and mise en place. Most complicated wokked dishes are cooked one or two things at a time, according to desired technique (liu, pao) and then assembled on the plate (or the to-go carton). You're familiar with this if you've ever bought Chinese food to go -- all the meat is either on the top or the bottom. Now you know why -- they're cooked separately. You can get away with doing this with Asian food because everything is cut so thin it cooks immediately -- or else it's partially pre-cooked.
Hope this helps,