Mazda 626 six cyl runs ok for 20mins then misfires and runs rough

First Check All Air hoses. Make sure no vacuum leak are present.
make sure your ignition coil are good. This will make engine idle roughly. For the rpm to high or to low maybe your air idler is no good. If you're car turn off it might be overheated. Check coolant level. Make your not mixing water with oil. Check the oil dipstick to verify. If like a milky color then it's mixing water with oil. This will car to stall and run roughly

code p0303 refers to cyl 3 misfire detected ===causes engine mechanical fault--wiring--ignition/fuel system--injector--ECT/MAF sensor--ECM
code p0316 refers to misfire detected during start up --first 1000 revs===causes --engine mechanical fault--wiring--ignition/furl system--injector
the common fault cause is ignition/ fuel system and injectors so I would be checking fuel pressure and injector systems for clean and wiring connections are good especially on no 3 injector.

Check to make sure you are TDC compression stroke on number 1 cylinder.

Might be time to get some r134a freon added. When the car sit's it will build up pressure and when the pump kicks on it looses the pressure and goes into safety mode to not burn up the pump. If you do it yourself get the dye and pag oil also with the freon. It is very tricky to do it yourself so follow instructions carefully. Then check with UV light to see if it's leaking.

your sylinoid on ur starter is going out

Being a 95 it dosent have OBD2 so it may not store a trouble code in the computer.
From the symptoms it sounds like either, Air flow sensor, O2 sensor
The O2 will not usually cause stalling under acceleration.

Pull your vacuum line off your fuel pressure regulator and see if it smells like gas in line or if gas runs out of the line.

Intake manifold gasket on 2.0 L 4 cyl. fails. most of the time is at number 2 cylinder , causes check engine light with lean codes and sometimes misfire codes . replace gasket & plugs disonnect battery or reset PCM (computer) VERY COMMON PROBLEM GOOD LUCK

low idle speed...or the need of a tune-up

if u go on yahoo.com type 1995 mazda 626 timing and click on search images you will see a picture of how to set it.