What is the estimated cost to have a "Last Will and Testament" drawn and who get keeps the copies to prove that the document does exists.

The estimated cost for a simple will should be less than $500. You can either keep the original documents yourself, or some attorneys provide safes in which they store their client's documents, and you are provided with a copy.  I usually also give an extra copy in case the client wants to keep it in an easily accessible place, or give it to the proposed executor.