Deep linking describes a link that points to a lower level page of a website. e.g. instead of linking to the top level page at http://magicmonster.com, the link may point directly to http://magicmonster.com/x
Transferring your domains between registrars can help consolidate all domains into one account. Registrars also charge different renewal rates so it may be cheaper to move.
You will have to request the 'auth code' from your original registrar before starting the process.
This is triggered from the original registrar. You should be able to tell them the new IPS Tag of your target registrar.