From what I understand about page rank its all related to internal linking and the page-rank of your incoming links (divided by the total number of links on that page). Is this correct? So, If you were to build a new site with 5 pages, with navigation at the top of all 5, and 1 link on each page that should build internal linking. Then if you get a solid high PR Backlink or 2 (as well as link to a few other pr 3 or 4 pages) this should build a lot of strength on your inbound and outbound linking. or.... am I just crazy here? lol.
Google doesn't update PageRank weekly, so no, it is not possible to get PageRank 1,2 or 4 within a week.
No, as previously stated Google doesn't update toolbar PR weekly ... it may well update internal PR weekly, daily, hourly (who knows). Toolbar PR is updated roughly every 3 months. Don't worry about PR .... it has little effect on where a site sits in the rankings ... concentrate on content and inbound links. Is there a reason you NEED PR3 or PR4 ... other than to impress people it has no real function for SEO purposes (a PR1 site can easily outrank a PR3 or PR4)
What is mention above is true. We know about Google PR from the RP button on Google toolbar, which updated approximately every 3 months. what happens in-between I believe just few people in Google can know. I suggest you to concentrate on content of your website and correctly tuned meta tags + titles - these factors will bring you traffic, not PR.
First off, no it's not possible because they update PR quarterly. No matter what your PR, you should definitely not be focusing on this. Focus on getting links from trusted sources in your niche... authoritative websites, directories (Yahoo, BOTW), blogs, article directories, press releases and good old fashion PR to get editorial links placed.....as well as continuing to add quality content to your site will pay off tons in the future and bring you rankings and traffic organically. PR is just an ego booster and it really means nothing.
Useful contents will bring more real traffic, and I think it is more important than PR. Absolutely agree with this one :
I believe the next Google PR is in April but you have to do both "on page"and "off page" SEO to get ranked on page one.
If you want to increase page rank, you should have consistent blog update (or content update in your website), it is good to have daily posts with XML sitemap submitted to Google webmaster. Most importantly, you should gather high PR dofollow backlinks to your site to increase page rank. There are possibilities to get PR1,2, or 3 within a week. If you know exactly when is the next PR update, then try to build high PR backlinks just a week before the update to your site. Getting PR5 or 6 dofollow backlink with high quality about a week or two before PR update, can get your new site with PR1+. The problem is, no one knows exactly when Google Page rank update takes place. Last update was on 30th December 2009. Next update is expected to be in April or end or March. So, it is experimental basis. You can try to build backlinks to your site until next Page rank update and check if your new site able to get some PR or not.
Well, I've never heard anyone claiming that it determined adwords costs before - you can throw that one away right now - no connection at all, whatsoever. There is a PageRank used 'behind the scenes', that is part of the algorithm - what's known as 'toolbar PageRank' , the PageRank they let you know about, isn't much more than a popularity contest. Other than that, well yes, getting high PR backlinks is how it's done. The internal linking scheme is a bit of a red herring, what you're suggesting isn't sophisticated enough to be called PageRank sculpting, and you have to have PR for your homepage to start with, for any to get passed to internal pages.
Pagerank is just an algorithm to rank pages. Don't let your site be defined by its pagerank. Rather, let the content in your site speak for itself. Good content usually brings in good pagerank but not vice versa.