there are many good coaches in the game,if you are managing high reputation club,you can get great coaches,so if he is not good anymore,just buy another.
Fire them all when you start managing the club, it is more likely they will accept a mutual termination at the very beginning. If there is a good one among them (usually that's not the case), you keep him of course.
I see a lot of regen staff, which I don't like and I try to avoid them when picking my staff members. I usually go for 30-60 years old coaches, with reputation as low as possible (so I get them on cheap salary).
Regarding the stats dropping, it's not normal but it happens. I mean they are staff, they don't get injured, they get older (and thus more experienced)... someone would expect their stats only to increase. Well, another bug of the game I guess.