The best way to boost your page rank is to get your URL listed and linked on other high ranked websites (doesn't have to be the same subject matter). The more your URL crops up when the bots do their crawl the higher importance/ranking your webpage is given.
It can take months and months though to build a good position. Also depends on whether your page is compliant with proper code use etc etc.
Yes it does. In order to get a proper rank and not a temp boost the referring site needs to be of the same subject.
Also, having valid pages helps but only a little bit.
It's all about content - if your site is good people will want to link to you and you'll get good rankings. Getting the ball rolling is the hard part.