The ex-employee that left google made no secret that googles #1 focus right now is making google+ succeed. So expect it to influence every other service they offer more and more in the future, in fact I believe you need a google+ account now to make a youtube account... Granted I think fcc still monitoring Google to see if they give unfair push to their own services right now, so they may hold off before they really give it heavy weight in search rankings.
I am not sure about this. Google+ is good social media site but not the best one. To pick the top position May be Google can do this.
I really the new feature of google+ authorship..I dont know about the others but it has worked out for me.. My site ranking is same but somehow my website visits have increased...
Yes it influencing ... but i guess when keep yourself signed in and search something on Google then it influences much ....
If I know well, it does in an indirect way. If someone +1s a page, then he and his friends will see that page in a better ranking if he is logged into his account.