Good Evening, Annie,
Dropping in a new mat should be about a three-second operation. There's ordinarily nothing but gravity to hold it in place. I believe that replacements are available from Seal or perhaps from Light Impressions, Calumet, or Dick Blick. You could probably also fashion a substitute from any material similar in density and thickness. Something a little thinner than the original would work fine if it's backed up with some plywood or Masonite.
I doubt that the material stuck to the platen would be a hazard, but you should plan to get rid of it anyway; the platen should be as smooth as possible, even when used with release paper and/or mounting boards between it and the target of the operation. Almost any imperfection has a way of transferring its impression to the face of mounted prints.
A couple of years ago, I was given (yes, given!) a Seal 210 press. It had a considerable amount of mounting adhesive at various places on the platen because the previous user(s) had neglected to use release paper or been careless in doing so. I spent seemingly endless hours cleaning the platen, using nothing but steel wool and isopropyl alcohol. It is a messy process; the old adhesive will come off, but a lot of elbow grease is required. Still, with a press as small as the one you're considering, the time and effort would be a lot less than with my 210. Seal makes a special platen cleaner; Calumet lists it at $31.99 for a 2 oz. jar! Perhaps it's more effective than alcohol, but isopropyl alcohol/steel wool seems like a better thing to try first.
You don't mention anything else, but I would check that the press is OK electrically (nothing frayed or obviously damaged), that it heats up OK and across the whole platen, and that the thermostat holds the temperature steady as selected. I would not pay big dollars for a press with the deficiencies you have noted.
I've used Seal presses for almost forty years; please feel free to send me a PM if you have other questions.