Answer: The truth of the matter is that most people would not replace these tires if they still appeared to be in very good condition, myself included. This would be especially true if you were only planning to use the car for local trips. The responsible answer would be to tell you that you should replace the tires. Conventional wisdom, and the tire manufacturers, believe that a tire cannot be structurally sound after thirty years. All it takes is one blow-out at highway speed and you will wish that you had invested in a new set of tires. Besides, what better time of year to buy yourself a gift?
The problem with your emergency brake is most likely vacuum related. The emergency brake is designed to be released by a vacuum switch when the shift lever is moved out of park into any other gear. There is a vacuum pod with a rubber diaphragm that is often the culprit, but it could also be as simple as a broken vacuum hose. These parts are generally available from any of the major classic Cadillac parts suppliers, but they are not inexpensive.
You do not mention hearing a hissing sound which is typical when these vacuum pods fail, or if a vacuum line breaks. In order to quiet the hissing sound, the vacuum source has to be plugged. Since someone apparently did this, it would lead me to believe that it is the pod that has failed, and not simply a broken vacuum hose.