I have read agot about Google+ and Google +1. Do these both have any connection regarding rankings in Google?
it will help you rank better on Google search engine. The more + you get the more it will increase you rank on google SERP.
In theory it would help you with you ranking. It's now still in the very early stage and nobody knows how it will effect the search result. Google had suggested that this is a social factor. For example, if your friend clicked +1 on a website, that sort of mean your friend is recommending it. Hence, Google will think it is more relevant to the keyword that you typed in. So, for this to even work, you would have to start out with lots and lots of friends on Google+. Then of course there are other factors too. You can read all about this in the Google webmaster central.
It helps your PR, I know that, but I don't know how it affects the rest of your SEO or how powerful this still relatively new initiative is in terms of social site advertising.
Certainly Google + helps in ranking. But it is only for Google. Not for Yahoo, Bing and other search engines.
Ok it's not a theory anymore Last time I read up about this, I only knew one case study who claimed that it helped (The one from mashable I think). This time I found another one. You can read up about it here: http://www.wordstream.com/blog/ws/2011/07/26/google-plus-vs-facebook-vs-twitter-vs-linkedin Code (markup):