I worked with big international brands, I've done keynotes all over europe and I write books about what I've learned.
How about a report button letting your users decide?
In my experience, yes. Dropbox did this with great success.
I would recommend that you check out http://wistia.com/ - I use them for all my videos. Public and privately.
You need to build up a list of emails. To do that you need to create a feel of exclusive access and that the one of the list might experience your product before everyone else. Also i would use Facebook ads to drive app installs.
I would recommend that you simply test this. And track the results. Your answer will be different for every product and target group one may have. So always faster and better to just do a test.
I would say that a good way is to value it by reach and engagement, also I would do some tests on how many of the people that see the link-posts click them.
Number of fans has no value, but engagement and being able to move traffic outside Facebook to your page has great value.