If I cancel my plan what happens to my existing files and links to designs. Also will I be able to access my .xd files at all? Will the links remain accessible?

If I remember correctly, Adobe will keep your links for 90-ish days after cancellation, but ultimately they will stop working. Files in your cloud storage should be fine if they are less than 5gb in total, as the free plan allows 5GB of storage. You will of course lose access to Xd and the ability to view and edit your .xd files. 

You can read more on it here.