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Do you have a Google Merchant Account? You need to set up a product data feed for your products to appear there.

Those reviews are not from Google marketplace (Google Merchant Center).  It's done through Rich Snippets. There are a few standards right now, namely microformats, microdata, RDFa, and Good Relations.  I've experimented with the RDFa tags to some success but haven't been able to achieve the reviews straight-up in all organic results.

Once you choose a format you can test your pages here.

Yep, they sure do.  You can find more here which briefly discusses site hierarchy and spreading link juice based on your domain weight.  Depending on your domain authority you might want to be more selective on the "widgets" you choose to link to, at least higher up on the page.

Motava, here's a video where Matt Cutts discuses the nofollow attribute on internal links.  Generally I'd agree with EGOL and say it's a bad idea to place nofollow tags on pages that you do want followed in other locations.

You could get fancy and place the links in a subfolder restricted by a robots.txt file and generate them via ajax or javascript, but that's probably not worth the added effort.

I agree with EGOL, unless your current URLs are absolutely driving you nuts, I'd leave as is.  Plus 301s never direct 100% of the link juice so you'd most likely be hurting yourself.

Hey Tom, although everything you're proposing below in regards to SEO is great, and should be done anyway, I don't think that's the reason you're seeing poor (or no) performance in Google Shopping.

Disclaimer, my knowledge of Google Product Search is limited to my experience in the U.S. There may be a whole different set of requirements for the UK.

Over the last few months Google Product Search has been rolling out additional requirements and perhaps their most recent update(s) affected you.  I can't say for sure, but I'd make sure you are providing every attribute possible that they request, even the 'suggested' attributes. Additionally, make sure you are not providing more than one record for each Unique Product Identifier. Glancing at your site, I could not find any product SKU / UPC, etc. associated with your products, but that doesn't mean you're not providing it to Google.

See here the the most recent update: Google Products Search Feed Specs/Policy Changes

Hope this helps.