real qick, when you make your own website, can you make your own game? I've been to dsicade and there a game called wakytap :D. i can see that someone made it.
“If you want to be fancy, hold your pinky finger like this. The higher you hold it, the fancier you are.â€
Assuming you're speaking of creating games on a limited web host designed for mobile browsers, then generally no. It's usually hard to import game code. Some hosts let you add pre-made games, but these are rarely DSi-compatible.
DSiCade and other websites can support things like original user-submitted games because they have their own domains.