Roman,
Here are my thoughts:
1. Can we PM our followers on twitter or facebook and directly ask? As long as you stick to people you know would be a brand advocate for you, I don't see why not.
2. Which medium is generally most successful? We've generally only done email, but primarily because that's how we communicate with them on a normal basis anyway.
3. What if we tweeted something like: "we need your help, anyone that leaves an honest review on yelp will get _____ (money, gift card, appreciation, etc.) - I know it's tempting and seems logical to make offers like that, but it violates Google's guidelines. Even if it's not for Google reviews, they might get wind of it and discount those reviews. Reviews are supposed to show a reflection of your business, not what you've offered in exchange for good reviews.
4. Which review site is the best for improving reputation and SERP- google plus, yelp, bbb? Those 3 are the top ones I'd stick to.
5. Would you recommend sending people to consumer affairs to try to offset the bad rating or to just focus on all the other review sites and have them usurp consumer affairs' position? Definitely try to get some better ratings on CA to cancel out the bad.