I am interested in purchasing a car with a few problems

If you don't know how to fix those things now, that isn't going to change by becoming the owner of the car. All of those things could have easy inexpensive fixes but they could also be very costly to fix. To start with, the diagnostics could take some time and that's what you're paying a mechanic for. You have to consider the cost of diagnostics into the cost of buying the car, and that is unknown, THEN you have to add in the cost of repair, and that too is unknown. If this car is being sold by a dealer, why didn't they fix these things first? If it's being sold by an individual, there's a reason they're giving up on it instead of fixing those things them self.

Not all of these things happened all at once either. Sounds like the previous owner just ignored things as they broke. Makes you wonder what else is wrong that they don't know about or aren't telling you. It sounds like all they told you is things they knew they couldn't hide. Unless you get it at a real good price and are willing to spend a lot of money fixing it, I recommend looking for something else with fewer problems.