I doubt it's a followed backlink.

Look at the backlink HTML to see If it has a nofollow on your URL.

A link is a link regardless if it is dofollow or nofollow. You need a mix of both to give your website a natural linking profile.

As to the PA/DA, that will depend on the page you get the link from. Either way, you can always boost that link to increase the PA by building links to it as well.

Check your webmaster tool and find out its count as a backlink or not. And check out DA , PA using Moz DA checker tool.

Yep you can use the Moz Bar tool to see what the DA and PA of page that is linking to you is.

Well here is my two cents. It depends on how relevant the link is. Nowadays i would prefer a link from blog that writes about the keywords i use over some big name website that links all over the place

If you are getting a link for a relevant text then it would be very much beneficial to you.