I've seen a lot of people getting event Pokemon so I tried it for myself and when I went to redeem one it never connected and showed that I wasn't connected to my wifi. The list people tend to give also never include the DSi or DSi XL
Yes, the exploit works on DSi for every Gen 4 and Gen 5 game. This includes DSi XL. I know because I've done it many times. Refer to this answer for help setting it up.
No, DS WiFi is discontinued
Source: experience