For D2E Wii you have quite few choice for modchips, D2pro9v3, Wasabi3, D2Sun, Wizard & D2E-A9, I believe all except the A9 can be solderless solution although the D2Pro9v3 and Wasabi3 "may" require a single solder point. Also I believe the D2Pro9 is the only one offering the option of programmable Actel h/w chip using JTag programmer D2Prog (sold separately) as well as SPI Flash update via DVD. All the others I think you can only update SPI flash via DVD, but I may be wrong on that.
1) Yes its fine to update wii to the latest version 3.3. You can even still install Homebrew channel at 3.3.
2) As I mentioned D2Pro9 has the optional JTag progammer for h/w update so I would consider that the most future proof, but saying that all the other chips are all working 100% and haven't had the need to update the h/w, but the D2Pro9 has needed to enable it to work with the different Wii Drive types. Hopefully SPI update via DVD would be the only thing required.
3) Yes you can currently play online and be connected to interent without affect wii, but no one noes what Nintendo will do in the future.