When link building, is it acceptable to link with a site that has high authority but has minimal relevancy to our site? - If you are being offered a link from a high authority site from a good industry - take it. You have already done all the work and Google is not great at discounting non-relevant links.
Also, if we are publishing articles on other sites, should we also publish them on our own site? Should we add "nofollow" if we publish them in our site? - My recommendation is publish great articles on your site first and foremost. And I would not distribute them. Why give others great content? If you are doing article distribution for links, then send out your "not so great" articles and link back to your appropriate webpages.