yes noindex,follow category and tag pages. It's the Yoast default setting i believe.

You are leaking your PR to these other websites, and if not opening in a new window, you're increasing your bounce rate and lowering the time spent on your site.

7 to 8 outbound links on an article is a tremendous drain of your internal PR and could also send Google the false signal that you are selling links since they are dofollow.

I would remove outgoing links, if you need them as references then nofollow them and target="_blank" them. You are still losing some PR with nofollowing them, but Google can read them and still see that you are linking to them if that is your intention. I would allow Google, FB links for example to be dofollow, but would no follow lesser known sites.

You mean in your sitemap.xml?

The canonical tag is a tab that goes on pages to let the bots know which URLs you want to get credit for content. So theoretically, your sitemap.xml file URLs should be very similar to your canonical links you are declaring in your metas.

I don't think so either, but you never know. Simple enough test to run to see if Google recognizes a "follow" or "dofollow" tag, simple enough test to run that's for sure. If it is hardcoded in the link code it will override any external nofollow tag.

test it to see if for some reason it is recognized, just for fun.

if something on a site is nofollowed by default and doesn't show up in the source code of that link (meaning it is declared in another piece of code), add a rel="follow" and a rel="dofollow" tag and see if it overrides the nofollow by using a firefox plugin tool that highlights nofollow links for you (you should already have this installed if you are an SEO)

The first question I would have is why?

"The issue here is when I combine my content widget with my shop widget page, no one buys anything."

You can include all of your content on the shop page and hide it in a jquery and the shop page would look almost identical to how it is now, but that page would rank because of the content and the user would be one click closer to the purchase than if they were to land on the information page first.

I would suggest doing that and only having one page per product with the information on the page in a way that does not negatively impact conversion rates. Some a/b testing may be in order, A/B testing is always in order anyway for conversion pages

If u get permission in writing then no problem, also I would check the copy to see if it's already transcribed somewhere. If it was then it's duplicate content

My guess would be that the creator of the content owns that content and you are still copying it. I wouldn't do it with a company who has deep pockets.