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Then somewhere on the web, there is a link to that page, i would 301 it to a relevant page

I don't think so.

A long time ago in first days of the internet websites were no more widley used than other protocols such as ftp or telnet. a domain may have sub domains such as ftp.example.com, telnet.example.com or www<a>.example.com</a>. but example.com itself would not be used, since then websites are the main protocole used and people started to make example.com respond to websites. so really we don't need www anymore but best to redirect it just in case

Get links from relevant websites, with high authority. Its hard to do, hard to fake, hard to manipulate, but if you create good content, sooner of later you will earn them.

They definately do pass page rank, it is just if it is internal links or external.

They would nott have pr of 100, becauce each page has its own page rank.

also As i stated above, if google can tell if a sites is on the same subject or on multiple subjects.

Take a look at these 2 results, the first word press conatins a sub domain in its sitelinks, but to the en(english subdomain), they can tell that that subdomain belongs to the root.

https://www.google.com.au/#hl=en&output=search&sclient=psy-ab&q=wordpress&oq=wordpress&aq=f&aqi=g4&aql=&gs_l=hp.3..0l4.1292.1292.0.1676.1.1.0.0.0.0.383.383.3-1.1.0...0.0.eJcS0C6Duts&pbx=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.,cf.osb&fp=7c4df592a329114b&biw=1280&bih=909

Have look at this result and yopu will see that many of these companies subdomains are listed as belonging to the same site

https://www.google.com.au/#hl=en&sclient=psy-ab&q=iboats&oq=iboats&aq=f&aqi=&aql=&gs_l=hp.3...146410.147314.1.147555.6.6.0.0.0.0.0.0..0.0...0.0.MLsJj78G5H8&pbx=1&bav=on.2,or.r_gc.r_pw.r_cp.r_qf.,cf.osb&fp=7c4df592a329114b&biw=1280&bih=909

this is simple. rather that test what the domain name is, test what it is not.

use the logic,

if not my-preferred-domainname then redirect to my-preferred-domainname.

Its just a notive to let you know they are there, Rel canonicals are somthing you would nort want in the wrong page, so letting you know where they are is a good thing

Obviously the second link is better.

My point is that the page the link was pointing to is no longer relevant, it is the link text and linking page that you need to consider.

I would not no index any pages, this sounds like a job for a canonical tag.

if you do decide to noindex pages, make sure you noindex,follow, you never want links pointing to no nofolow pages as they pour away link juice into the ether. if you make sure they are follow the link juice will pour back thought the out links on the pages.

I crawled your site and did not find any links pointing to those urls.

I did find a lot of other problems, the worse being 100 broken links, and 160 unnecessary redirects.

not sure what rogerbot does here, but i would definatly 301 rather then use rel canonical, if they have no incomming links i would let them 404

i would not worry about PR, all pages have some PR and all is usefull.

i would make sure none of tthe links come from sites that may harm, you spam or porn sites. If they have little PR and are not relevant, then i would not worry about them, but as long as they are not spam paid links they will not harm you.

This page may exlain a bit more abount pr.

http://thatsit.com.au/seo/tutorials/a-simple-explanation-of-pagerank

Patrick makes some good suggestions, one other thing you can try, is to try and place the form in a iframe, then you can use the iframe page for your sitelinks.

It is 300 keywords for all campaigns just to be clear.

You should report it using the feedback tab, on the left, it will be fixed pretty quick

Here is what works for me, with very few links.

Make sure your site score a perfect crawling score, I use the Bing api (you can get most of this using Bing WMT or IIS SEO Toolkit) for this. You will never get a perfect score using a CMS.

Use html5 tags and schema.org to clearly mark out your content, leave the search engine in no doubt what the page is about, and what is what in the page, once again you will never achieve perfection here with a CMS.

Use internal linking to it full potential.

Have original content, make sure it is clear and do not over optimize it, fine line here.

In short have good content clearly marked up as to what each peace is(html5 schema.org), clean code so that the search engine can easily work out what the page is about, what is content and what is layout.

There s a lot yopu can do with internal links including giving relevance to a page and pushing your PR aound the site. you can not increase the sites PR by internal linking, but you can make some pages rank higher at the exspence of others.

http://perthseocompany.com.au/seo/tutorials/a-simple-explanation-of-pagerank

Imaging a page with 5 links

link1 to domainA

link2 to domainA

link3 to domainA

link4 to domainB

link5 to domainB "no follow"

60% of link juice will go to domainA

20% will go to domainB

20% will be wasted (no-follow)

The link text for link1 and link4 will pass link text relevancy, the other link text will not pass any relevancy.

Its a bit more complicated than this because the first link passed a bit more then the last.

read http://thatsit.com.au/seo/tutorials/a-simple-explanation-of-pagerank

Your first problem

Look at this page,

http://thermalunderwear.eu/eng/kids-thermal-underwear/coldpruf-enthusiast-kids-thermal-shirt

you will see a link to http://thermalunderwear.eu/kids-thermal-underwear/coldpruf-enthusiast-kids-thermal-shirt

I will look at your other porblem in a few minutes

since the sites structure will be different, you are probably only going to get PR  from links to the home page.

PageRank is passed by links, so any links pointing to the PR6 domain can now point to your domain. But there is more than page rank, there is relevancy. If the PR6 domain was about cats, they the link text and linking pages are probably about cats, if your site is about cars then you wont get any relevancy.

as for the mentions of link building, as I stated above, PR is simple links, the PR6 domain much have a lot of good links already.

Shane is correct in his advice,

Q1

you dont need the canonical, if you did not have a 301 redirect, then the canonical should be on the old page pointing to the new. but as Shane said you dont need it when you have a 301 in place.

Q2

I would canonical to http://www.example.com/new-widget-category for all p1 to p5

As i wonder if the change of the products in the grid is enouth to make the pages unique. If you have sorting it just gets more messy

Your product pages will have this info for each product anyhow.

i would try to make the category page relevant for the catgory.

Rather then use rel=canonical I would use rel=next and rel=previous

http://support.google.com/webmasters/bin/answer.py?hl=en&answer=1663744

David is correct, it can look like link farming. but only if you do it a lot.
but the bigger concern is that you are pouring away link juice. Its like I give you 10 dollars and you giving me 10 dollars, where is the gain?

Make a query, go to bottom of page, and click on advanced search, select 100 pages.