If someone has a public 'right of way' written into his deed(or mortgage), does that make it his?

Your question concerning a right of way, or easement cannot be answered without looking at the document that created the easement. I am guessing the neighbor owns land, subject to an easement which gives you the right of use. Having a easement for access (often referred to as ingress, egress, and regress) does not give you the right to park cars. On the other hand, if the prior owners of your house had adversely used the area to park for 14 years, when added to your 7 years, there may be a prescriptive easement. DO NOT discuss this with your neighbor until you first talk to a lawyer. Adverse possession and prescriptive easements are often destroyed by asking the neighbor the wrong question.

I agree with my colleague. You should consult with a local real estate attorney to determine if a right of way exists and what your rights are to it.

I also agree with the other attorneys. You should speak with a local attorney before speaking with your neighbor. Doing so without discussing it with a lawyer could have adverse consequences.