Frankly speaking links on both the sites, DONOT WORK, until and unless you have some smart ways to do it. Just posting links on facebook and twitter will not help you at all. For example before posting links on facebook you need to have a profile filled with lots of targeted friends of your niche you will be interested in viewing your site. You should be having a good and healthy fan page with lots of fans who like your page. So you can do some marketing by posting some stuff in the fan page wall. On the other hand, it goes same for twitter, just posting links will not help you at all. You need to have lots of followers under your belt
if they're nofollow, so why G webmaster tools recognize them? if G can see them, post links to your website from fanpage often, eg. link new content from blog.
They help with indexing. I wouldn't put any weightinto them as far as SEO and building links. But to get web properties/other backlinks indexed, twtiter is a great tool
Facebook and twitter have PR 10 and 9 respectively. Your link at such high PR sites obviously works. More ever you also get good amount of traffic from these social media sites.
Even if FB and Twitter value links like dofollow they will give a zero value to your website, cuz there are huge amount of links there.
Facebook and twitter provide nofollow links only. They don't help your website in SERPs ranking but you can get a lot of targeted visitors for your website. YOur ultimate goal is to have traffic on your site and both websites (facebook and twitter) will give you that.
I have read somewhere that the social networks like facebook and twitter may have a positive influence on SEO. So the answer it is : YES, facebook links WORK.
Yes it do work while you can find some search result from google search that link to facebook. In the future, facebook would add a search engine search beside the facebook search . But they both use the same method which they recognize keywords and facebook recognize with the most popular post or profile or fan page.