Do you have goals set up already?  If so, go to your organic traffic section, and right above the graph on the left you can select which goal set.  This will change the settings for the lists below the graph, and allow you to see the conversion rates based on keywords.

However, that won't work unless you have your goals set up.

Can you search for the products on the home page?

How much filtering would it take to find the product I'm looking for?

During a presentation at Pubcon, several experts said that the 2-3 clicks or less rule isn't true, and that you can get people to click more as long as the experience was beneficial and enjoyable.

Terrible example: I took over a website that forced you to fill out a search box before you were ever able to see the inventory.  To make matters worse, you actually had to fill one of the boxes before you could move ahead.  It was terrible for people just trying to browse my products.

However, being able to filter my searches when clothes shopping online is a life saver.  I'm a bigger guy, and don't like several colors.  So, I'm able to filter by size, style, color, etc. to be able to find what I want.  Each of those is a click.  I'd say the same thing about computer hardware.

The only real way to tell is by testing the website.  There are a few different programs out there where you can tell people the end result you want, and they have to try navigate the website.  You'll get a recording of their screen, as well as them speaking about the process.  These people are brutally honest, so try not to take offense ever.

If it had a good reason to be there, and you had a decent link profile, then you are probably safe.  Even so, I'd say try to limit them to relevant pages.

The real question, though, is how much traffic is driving?  If it is driving a lot of good traffic that converts, then you pretty much have to leave it there.

Even prior to reading that I would agree with your analysis.  2 links from separate domains are better than 2 links from the same root domain.

This article talks about a website that received the Penguin penalty, and was able to start recovering by reducing the amount of site wide links: http://searchenginewatch.com/article/2180722/Google-Penguin-1.1-Pushed-Out-As-Some-Sites-Report-Recovery

"A) Remove all of the crap sitewide links, weird anchors first, B) continue building good links and C) take advantage of press by pinging Danny Sullivan to try and get it featured on SEL to get in front of Google. Obviously A) was not going to be completely possible so I was going for "remove most of your crappy links."

So, I do believe that site wide links are bad, and that it would be better to limit the number of links.  Also, here is a reference about the diminishing returns on several links from one domain: http://www.seomoz.org/blog/understanding-link-based-spam-analysis-techniques

"The first link from a domain carries the first vote and getting additional links from one particular domain will continue to increase the total value from a domain, but only to a point. Eventually inbound links from the same domain will continue to experience diminishing returns. Going from 1 link to 3 links from a domain will have more of an effect than 101 links to 103 links."

1. To answer your first question, it does count all the links.  However, there is a massive diminishing return for anything over 2 links on one site.  So, having 1,000 links from one site would not be beneficial.  Instead, have them change it so you get one link on their top two pages, and none anywhere else.  You can use Opensiteexplorer.org and the top landing pages tab to find which two pages to request a link from.

2. A sub-domain is a separate site, and would therefor have its own ranking ecosystem.  Even a www.abc.edu is a sub-domain of abc.edu.  So, getting a link from a sub-domain would be as beneficial, everything else being equal, as getting it from the root domain.   Just make sure it's just a link or two, and not site wide like you suggested you currently have.