Msp misfiring, overheating, etc. Help!

Hey guys, I own an MP3 naturally aspirated engine for years now and have never had any problems. Now, I have just purchased another Mazda to my car collection but this time an 03 MSP with several problems. I'll really appreciate your inputs and help.

At the time before buying the car, the previous owner did say he had problems with the car overheating. I searched up the forums before buying the car and had seen people mention how it could be the thermostat, warped head, radiator, hoses, or that the cooling system simply needed burping. So I didn't think it would be that bad. The car also had the check engine light on.(I will talk more about the check engine light after the overheating).
Driving the car home when purchased that evening, I had to drive 1 hour to get the car home. About 40 minutes into the trip, the temperature needle goes from normal to HOT so I immediately pulled over and shut the engine off. The coolant reservoir was boiling and smoke coming out of it. Once the car cooled down, I refilled the coolant with the car on and then began driving again. 5 minutes out of my house the same thing happened so I repeated the process over again until I got home.
I left the car off until the next day when I got home from work. I took a look at it, couldn't really see any possible leaks anywhere. I went and bought a failsafe thermostat at AutoZone in my other car, came back, changed it, refilled the coolant, and took the car back out for a long drive.
About 30-40 minutes into the drive, the car began to overheat again. Once again, I pull off to the side of the road and let it cool down and poured coolant while the car engine was running. Drove back home and as getting home it began to heat up again but luckily made it to my driveway and shut the car off.
So, I am a week sunce I have bought the car and can't figure out the problem. I just don't wanna spend more money without tackling the main overheating problem. Please Help!

Now to the check engine light. So several codes popped up when checked with the scanner.
P0090- FUEL PRESSURE REGULATOR
P0660- SECONDARY SHUTTER VALVE (INTAKE MANIFOLD)
P0480- COOLONG FAN 1 CONTROL CIRCUIT
P0303- MISFIRE CYLINDER #3

AT THIS POINT I AM FRUSTRATED AND DON'T KNOW WHAT TO DO.
The car feels like it jerks when I accelerate hard. As if it wasn't getting any fuel or something. Car does have a fmic and some other mods the previous owner did to the car. Car only has 112k miles. But all these problems are just ongoing. Please help on what to do. I have never owned a turbo vehicle so I am not familiar with the system.

The overheating is probably from the cooling fan, is it coming on? Turn the AC on and pop the hood to check that both fans are running. The P0090 and P0660 are more than likely the solenoids on top of the intake manifold, brown plug is the FPR (P0090) and I believe the 660 is the VICS (white plug). The misfire is either the plug or the coil pack, which is why the car is jerking under acceleration. All of these issues are easy fixes

Yes, both fans are coming on. I did check. The plugs above the manifold I will have to check. I have already changed the coil packs+spark plugs&wires, coolant temp sensor, and thermostat.

I took it in to the shop that a buddy of mine recommended and the one service technician took a look at the car and found oil mixed with water under the oil cap. The coolant/water in the radiator bubbled once the rad cap was removed. Therefore to believe that the head gasket is bad unfortunately. I will have him do the work for me.
Where can I get a good head gasket set? Not stock, maybe a good high performance set??
I appreciate your help and input.

A felpro head gasket will be fine, rockauto had a sale on them a while back. I got head bolts and the gasket for less than $50. They sell a kit that includes all the gaskets you need. Be sure to get new bolts too, DNJ and felpro sell them for about $20, OEM are over $200. I have used both the felpro and DNJ and they both worked fine. It's really not that hard to do by yourself if you want to save some cash. Did you regap the spark plugs when you installed them? The NA proteges use a .044 gap but the MSP needs a .028 gap and most parts lists are incorrect so it's common for people to install incorrectly gapped plugs.
If there is a CEL for the fan there has to be a fault somewhere, I am guessing the fans are not coming on while driving which is causing the overheating. Could be the relay. And typically the fail safe thermostats are not a good idea, once they pop open they do not close anymore.

Ok, I will have to see what they have as far as the head gasket set. I appreciate your time and advice.
The spark plugs are wrong then, I had searched up the gap for the spark plugs and I got them .044. So I would have to get back in there and change them to .028. Therefore, mine are gapped incorrectly. I will continue to check if the fans turn on while driving. I know once the car come to a stop I can feel them running. But haven't really focused on if they are on while car is running.
About the thermostat, would you consider me changing that one back out and just sticking to the non fail safe one that doesn't pop open ?