My question is a threefold one:
A) When should I start feuding? I don't want to make creative do all the thinking on my behalf. Do I just enjoy the random matches until something pops up or what?
When you have an idea. Your open challenge idea could work, though that's hard to pull off with the nature of e-feds and how easy it is to be outdone even when you put out a solid RP.
Just take a look at the roster and think about who you would like to work with. Come up with a plan for the feud and write a PM to a member of creative with the details of the feud. You may want to check with the person you're feuding with before you tell creative, but that's not always necessary.
You might want to try and stick with people in your part of the card: Krypto, Alhazred, Carnival of Carnage, Vega, Jimmy Flynn, Sandy Deserts, Isabella Stone... these are all options for Grizzly Bob. I think a feud with him and Jimmy Flynn could definitely work as the Flynn could be the disciplined wrestler where Grizzly Bob is equally into the thrill of sport, but has a much wilder approach to it.
B) Beard and I had a little face-face battle. He's happily involved with Gent, so I can neither team or feud with him. The four wrestlers who eliminated Grizzly are Drake, Vega, Celeste and Chris KO. Vega has a vice-like grip on the Mayhem title, so asking for that feud would be stupid. The rest all have their own things going on AND would outclass Grizzly so badly... Same goes for Rush.
I don't know if I'm ready to commit to a tag-partner AND there are many face teams like you and JGlass already, so a tag-team looks out of he question. The trouble is, the only other undercarders that play heel are in a tag-team, so what would be a good move?
Forming a tag team isn't out of the question. TBK (Gent) is taking a break, so Beard may be looking for a new buddy, but maybe you can form a team with Flynn instead of feuding, or maybe do an odd-couple thing with Krypto. Carnival of Carnage isn't exactly ready to feud with the likes of Saxton/Saboteur or Technosa (not trying to put them down, they're just such a new team), and a lower card tag team feud could help establish either team in the division. Tag team RP'ing may be more of a challenge than singles RP'ing, but it also allows you tell longer or more fleshed out stories if that's what you're into.
C) What I was thinking, was the Wade Barrett "Open for business" approach, but that'd require very good RP's on my part to not look like a total fool. Would this be doable?
I don't think it would make a lot of sense in kayfabe. What has Grizzly Bob done to attract challengers? Also, Chris KO briefly ran that angle, and it did not work out well for him.
The important thing here is to just let your imagination run wild. People are probably tired of hearing this from me, but my first major feud was with Action Saxton, and it was for a spoon. This is fake fake wrestling, and almost nothing is off the table.