Should I get specific backlinks for my whitehat SEO site? and different for my micro niche blog?
Short answer: yes.
Long answer: It depends on your site's age, niche, current link velocity, current link profile, etc. on whether or not unrelated and different levels of authority links will make a difference for your website or not.
Backlinks all have different values according to most people on the web. One backlink from a PR4 site is worth more than two backlinks from PR2 sites.
Partially true.
The authority of the site hosting the link gives the backlink its juice. This is why .gov and .edu sites are prized since they seem to be higher ranking pages and have fewer links going out.
Page Rank is a "general" indicator of a web page's worth in Google's eyes. What you see in the tool bar is rarely updated even though page rank changes daily. A snapshot of it use to be sent out to the Google toolbar every 3 months or so, but last year it didn't even get it that often.
PR of the root domain is only a general idea of its strength and authority, and should only be used as a general assumption of a link's worth. Getting 2 links on two different pages of that PR4 domain that have little to no PR themselves may or may not (usually not) do anything for you while getting 1 link on a page that has a PR of 4 on a PR2 domain may give you a lot of benefit.
Another theory is that each site only has a limited amount of linkjuice and each backlink posted on it takes away from the juice pile. In other words, linkfarms and forum profiles dont carry as much weight as a backlnk from a site that only has 50 outgoing links.
This is the more logical and correct assumption to make. It's always on the page-level though, not the site-level.
What you need to visualize is that a site has all these links pointing to it, from the site itself to other pages, and from other pages on other sites pointing to pages of its own site.
All those links share a certain context. The context is defined by many different things, and each Search Engine bot defines it deferently: anchor text of the link, text around the link relating to the anchor text, the text on the page receiving the link in relation to the anchor text of the link on the giving page, position of the link on the page, etc.
All of that works together to determine the strength of the page. Each link passes a certain amount of authority for certain keywords/categories. So, you'd get more authority passed if you put a link to your page about dogs on a blog page about miniature hairless poodles that has lots of links also about that and text on the page about that than if you put a link on their page to your page about computers.
In the end, it is all theory since none of us work for Google and can not give you an answer based on fact.
Yup. All you can do is test, test, and test some more - jotting down what you notice and trying to see how it all fits together to give you a better idea of how to take what you learn and apply it in other areas.