In smaller towns you can park sensibly just about anywhere without charge. In the cities you'll need to buy an all day parking permit to park anywhere in the city's car parks. Without it you will be clamped.
Paid parking is only prevalent in the cities but you may find people will try it on wherever you park saying they own the land etc. You must buy an all day parking permit to park in municipal car parks in the cities and major towns.
Enforcement of parking is done by the police or by owners of private parking areas. There are no traffic wardens and there seems to be a prevalence of 'freelance' parking attendants who earn a commission from clamping and towing companies.
There are no specific parking spaces for disabled drivers in Kenyan car parks.