Welcome to the Q&A Forum

If you get a backlink, probably your document will be correctly seen as the cluster representative. Sometimes it can happen that your content is filtered (but there is no duplicate penalty) because the syndicating site is more authoritative than yours, or if your indexation frequency is lower than its and so the syndicate content is indexed before the original one.

If they use the unedited feed, however, you can get some deeplinks if you have internal linking in your contents.

If the second link goes to the same url, the anchor text will be ignored. If you are looking for local ranking, I'd suggest pointing the second link to the page containing your physical address.

When Google finds more than one document (ie URL) with the same content, it has to define which of them is the representative document of the cluster. In doing this it looks at inbound link metrics, essentially, plus date of the page, pagerank and other factors. In this decision, it can be wrong, indexing a page that can hurt you indexation (consider this situation: it indexes as representative document page 2 of a listing page in descending order: new items in this category end to be at page 2 or later and are less likely to be discovered).

The canonical tag can be a good solution, even if it is a hint and not a rule to Google...

I'd not remove pages from a site (unless they are duplicated, or void): the more the pages, the more the PR internal flow (if you a have a well designed site architecture).

I agree with David: building some authoritative links from many different resources is the way to improve your DA.