You need to buy a flash cart. There are tons available, the best for applications being the M3 range.
you could use search to find an answer... some homebrew is just copied to the root of your mem card, most games need patching depending on a flashcard you're using...
It doesn't need to connect to a computer. Besides, it's actually got a game library worth playing, unlike the PSP which only has homebrew and emulation going for it. If you're just going to spout nonsense, just leave the DS forum...
The range according to nintendo is the same, however since having my DS Lite the connection to my router seems much better from my bedroom, and my connection to my brothers DS is noticably better (we can now play between our rooms, instead of one of us having to sit in the others room)