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I've noticed nofollow links showing up in my Google Webmaster tools "links to your site" list. Google shows all of the links.  Followed and nofollowed.  I see nofollowed links on my GWT also. If they are nofollow why are they showing up here? Because Google is showing you the links to your site - all of them that can be sipdered. Do nofollow links still count as a backlink and transfer PR and authority? Google says that they don't transfer PR.  Do they transfer anything else?  Maybe, but only Google knows for sure.

The biggest advantage to running a blog-style homepage is that returning visitors will immediately see when you have something new.  This could lead to increased user engagement, more links, more likes, etc. A possible disadvantage will be that it changes your on-page optimization.  However, all of your off-page assets will be the same for a blog-style or a static homepage.  So as long as your title tag and heading remain the same you will have almost all of original optimization in place.  And, if Google gives any credit for "freshness" you will have that as often as you add new posts to your blog. All of my blogs have a blog-style homepage.  I think that it is a smart idea and the more often you publish new posts the more valuable that format becomes. Consider for your homepage a "most recent" and a "most popular" column.  This will allow you to feature "what's new" for returning visitors and show first time visitors your historical best content.