Yes! The government provides full medical coverage, if you paying the taxes. But the healthcare in the country is terrible, I mean the government doesn't pay much attention to health care system, so the hospitals and the doctors overwhelmed, underpaid, queues are too long. Sometimes you need pay some gratuities for the doctors (in the public hospitals) (but sometimes if you want to pay, they will refuse and be offended)
Otherwise there is no restriction, if you need a dental care, go to your district dentistry. Most doctors have private trades(?) as well, but I have no experience these.
The second, no we haven't liability insurance, only for car owners. So if you do something and you will need to pay for it, it will be deducted from you salary or if not possible you sentenced for prison (if you think about it).
So if the company you are going to work with have a Medicover or any private/company scale insurance then OK,
if the company haven't any special insurance , in most cases OK, but sometimes surprises can come.
if your salary is really good, you can choose private hospitals and doctors too.
I hope I helped with the answer