starting with the White Hat / Black Hat question. This harks back to the good old Western Movies where the 'good' guys all wore White Hats and the 'bad' guys all wore black hats.
In SEO terms; if you follow the 'rules' (guidelines) of the search engines then these are White Hat techniques; if you try to 'cheat' (game) the system then you are using Black Hat tecniques.
(Of course this totally ignores real life where to be successful in SEO you probably need a hit of Grey in there
With regards to PR this is entirely dependent upon the backlinks (links from other sites to you) you have coming to your site. A proportion of the PR from any page linking to one of your pages is 'passed' to you.
So, to get more PR to your page, you need more links in. HOWEVER!!!!!!
However, don't focus on the PR that you can see; not only is it not accurate it is only refressed two or three times a year. I only use is as a GUIDE as to how likely someone elses page is to be crawled if I get a link on there. High PR means that my link MAY be found more quickly than on a page with low PR. (But even this is a guide only).
When it comes to building links, basically, stay away from Black Hat tricks; if you don't know what you are doing REALLY WELL this will only lead to problems later.
Stick to looking for opportunities to place links where your customers are likely to see the link, (some pages like directories have 100s or 1000s of links on a page - just how likely is your link to be seen?), be interested in clicking it (so on a page relevant to your topic), and be likely to do business with you.