I've done it all before, including a full MTB build last summer. (Link is in my sig if you want to see what parts I used.) All the stuff I bought is genuine, but I am not sure if it's grey market or what.

If you're going to buy from China or Taiwan, Ebay is your safest way to do so BY FAR. You can see the reputation of each seller, recent comments, and they are incented to provide the right product and good service. Failing in all that you have Ebay to go to bat for you, which they are strong advocates for buyers because buyers make the system work. (Comparatively, they care a lot less about seller's rights, letting poor buyers run roughshod such as failure to pay, leaving negative feedback for trivial reasons, etc. But I digress.)

If you buy from a website not only does that stuff not apply, but also it could be outright fraudulent. The ONLY asian website I would buy from, and I have, is DealExtreme. Those guys are legit. I am sure there are others, but I haven't used them.

In regards to warranty, it depends. Don't count on anything, first of all. I haven't had to make any claims yet. But honestly I have never had a problem getting support if I needed it, from companies like SRAM. If you buy a complete bike or even frameset from Ebay from a major manufacturer you should expect to have no warranty, since all of the mfgs (that I know of) do not support internet sales or sales through an unauthorized reseller.