I have had my website up for three months now but only within the last two weeks have I been able to get a few other related websites to link to me. I still have a Google page rank of 0. How long does it usually take for page rank to go up?
If your pages appear in the index because of links from other sites, then you do have pagerank. But the pagerank number displayed in the Google Toolbar is not updated frequently, so it may take several months before you can see today's pagerank for your site. The number shown there is almost always more than a month out of date.
I also read at WebMasterWorld that page rank no longer matters. Is this true?
That is an over-simplification. Pagerank is important. But pagerank is only one of hundreds of ranking factors that Google uses.
If I type www.mywebsite.com, mywebsite.com or www.mywebsite.com/ my website will display. Is it true that Google will penalize you for having duplicate websites and that I need to have my webhost do some kind of 301 redirect (whatever that is)?
Yes, either you or your host needs to 301-redirect [w3.org] to the single version of your domain that you choose to use for linking to and advertising your site. Otherwise, your pagerank (and link popularity in other search engines) will be divided among the various versions of your domain name.
Be aware that since example.com and www.example.com are not the same thing, it is quite possible that two different Web sites will be at those two addresses. And "www" is a subdomain just like any other. For example, I use the www.example.com, test.example.com, and mobi.example.com subdomains of my domain as three completely-different Web sites (for the main Web site, testing site, and mobile Web site).
Added link to HTTP Protocol 301 Redirect description
[edited by: jdMorgan at 2:09 am (utc) on July 12, 2007]