1. Looks like you've found a loophole then! But it would be a good idea to ask and double check, so that your entry doesn't get turned down.
2. Normally, I update after I get a badge, but keep in mind I play rather slowly. When I update, I just post my game, player name, number of badges, current team, and usually talk about what I've done since my last update. Also, make sure that you don't double post when updating. If you have an update, but no one has posted since you last did, just click the edit button and add in your other update.
3. You can, as long as they fit the signature rules, which you can see and ask about here:
http://www.pokecommunity.com/showthread.php?t=267370
4. No time limits! They aren't races. There are rare occasions where a challenge will have a time limit though, and if you can't participate because of work, it's be to not participate. Challenge events usually last a month, which has been plenty of time in the past. We haven't had an event recently, though I have one planned for some time in the fall. Good stuff! You can see an archive of old events in the FAQ.
Anything else you need to know? :)