If the person selling the car passes state inspection, does that mean that it is safe to buy?

A state inspection performed by a mechanic at your request will find most mechanical and safety issues but the mechanic needs to go beyound the basic inspection and check the engine and transmission for excessive wear and any possible performance issues also.

The important thing its to identify any areas which require service immediately or very soon, and put a price tag on those services which you can use as a negotiating tool.

No it dont, Because a car pass the inspection dont mean that is safe to buy it, there could be other problems. The best way to find out about that is to do a carfax on it and that can tell you everything you need to know about any car you want as long as you have the vin number and year and make of the car.

If you ask that it is safe to buy, I wouldn't go for it, since State Inspections are basically done as on the road car tests, like braking distance, power steering, turn signals, wipers and so for, but mechanically it is impossible to determine, unless a general check-up is done by a mechanic. Usually, cars presented for Inspections are in apparently good condition for passing the test purposes, but later on they might develop a lot of problems, so my advise is that you don't trust in the fact of that it pass.

No. Maybe he has a buddy that does inspections, you don't know. All it means is that it has an inspection sticker. You need to have a used vehicle inspected by someone who knows what they are doing before you buy.