As a car gets older, will its compression ratio change? How about the MEP?

When the car gets older then compression ratio of car depends on the condition of cylinders. If carbon particle will not accumulate on the cylinders wall then the compression ratio will remain constant but if If carbon particle will accumulate on the cylinders wall then the compression ratio will increases.

So we can say that yes compression changes when car gets older.

On the other hand the mean effective pressure will decreases when car gets older due to wear and tear.