Hi neh004, welcome to the WiiHAcks community.
1) yes currently its ok to connect a modded wii to internet/online/wiiconnect24
2) Generally yes its ok to update online even if Wii is modded, its actually recommended rather than risking updating from a game disc of another region which would brick the Wii. But your 3rd question puts a twist to this.
3) This I'm not certain about, if you used Anyregionchanger to change the Wii entirly to NTSC-U including fm, language, region, then it may be ok but I have not heard of a case like this so I couldn't really tell you 100%. Also you might want to hold off on updating as a new update was just released and more information is coming as to what exactly this update will do and how it will affect a modded/hacked wii. So wait a while.