We know that when you change the permalink structure of a site, that page loses it's "button count" for Facebook likes, Tweets, and LinkedIn shares. The Facebook opengraph doesn't currently support any sort of URL changes, regardless of redirects in place on the site itself.

It is very hard to say whether or not Google has implemented the ability to (A) detect a 301 redirect, (B) check the opengraph stats for that former URL (since they can't check twitter or linkedin to my knowledge), and (C) apply those stats to the new URL. This is essentially the process that they'd have to go through in order to pass any value from social likes, etc.

I haven't seen any testing that would suggest either way. My hunch is that they don't.

10-15 dropdown links per tab is a lot to fit on the screen, but in my opinion the "too many links on the page" error is a bit overdone. How many total links appear on your pages on average? Unless you're blowing way past the general rule of thumb of 100 links, you're ok.

E.G. if most of your pages have 100-120 or less then don't worry about it. If most of your pages have upwards of 150+ links then definitely reassess how useful each link is to the user, and consider cutting down.

Here's an in-depth answer by Dr. Pete: http://www.seomoz.org/blog/how-many-links-is-too-many