As the parent company, I would want any individual work done to benefit the main site and as a store owner, I would want to have some benefit from the parent company as well. There need to be policies in place to prevent bad practices, but it should be all stores and the parent company helping each other. If they want to be treated as a separate entity then they should probably build a website themselves on a separate domain. Most major retailers have the stores in subfolders. Go check walmart.com as an example.

Best for SEO is with a subdirectory. Subdomains can be treated as separate websites.

You might try pinging the site out or just building a link to the site.

Quick fix = do the redirects.

Best practice = do the redirects and try to get the inbound links changed as well.

It is best if you can get the links changed, but always be sure to do redirects as well as there may be other links that you are not aware of.

I would recommend Screaming Frog as well, but a couple free alternatives were recently mentioned in a YOUMOZ post, http://moz.com/ugc/conduct-a-backlink-profile-analysis-with-excel-case-study