I think it makes sense that Google +1s is used in high search rankings. It's the one social signal they can audit to see if people are cheating on it. They own the whole Google+ social graph and can easily detect if it's being gamed.
Or it can just be that the more +1's you get, the more links you get, which boosts the rankings. So it may just be an indirect correlation.
No, I don't think so. Humbly, my best articles are the one with less +1s while the ones with relatively high +1s are related to my success or luck promoting them.
Also I don't see a correlation in my blogs between more retweets and more Google's +1s. It is most probable because my blogs don't have many visitors and didn't cross the charm, but I expect search engines like Google to leverage the long tail instead of smashing it.
I tend to see negative correlation between shares on any social media platform x and any social media platform y. The audiences just differ so much that anything that'll grab the Twitter crowd will tend to put off the StumbleUpon crowd, and so on.
There's some crossover between a very few platforms, e.g. posts which get a lot of InShares will also likely get Tweeted a lot. It's quite rare, though, in my experience.