Here in Costa Rica we have excellent medical care and if you were to get sick or have some kind of an accident while traveling. Nevertheless, while much more reasonable than in the US, medicine and treatment here can be expensive therefore we highly recommend insurance. No it is not necessary to bring water from your home. Water is usually safe in San Jose and the highlands. Where you have to be the most careful is on the coasts.
Bottled water is also readily available at most hotels as well as corner stores, and super markets.
In the past there have been repeated incidents of rented cars being broken into and a few cases of bandits flagging down cars and assaulting the occupants. Rented vehicles are identifies by special license plates and a sticker therefore becoming an easy target. So to answer the question, no it is not safe, but preventive measures can insure your safety and the vehicles. When in San Jose always park the car in a parking lot and never leave suitcases, camera equipment, jackets or anything interesting in the car. When out of town be sure to ask at the hotels if their parking lot has a guard and if not where the safest place to leave it is.