I have problem with idle every time I stop.
Everything is fine while driving but when fully stopped on traffic light the RPMs goes to ~500, keeps it for about 5sec. then slowly goes to 760 RPM.
It happens ONLY when stop after driving and right after engine start.
It does not happen on cold engine
Sometimes I got P0131 and P0455 error codes.
Also when I'm on highway >100km/h feels like engine has no power. In few seconds everything goes back to normal.
Any ideas where I can start?

 

how old is your Protege and how many miles are on it?
Did you read the https://www.mazdaforum.com/forum/maz...g%C3%A9-31136/

 

Mazda Protege 2001 ES 2.0
200000km

 

Give it a full & proper tune up. Including a compression test and a full vacuum leak check.

 

Do what grim said.

In detail: check for vacuum leaks, in particular for cracks in the air intake hose, clean the MAF sensor and the throttle body including the idle air control valve.

P0455 means there is a large leak in the evaporative system. That could be anything from a bad gas cap seal to broken hoses to the charcoal canister.

Give it new spark plugs (the correct kind with the correct gap). I believe this engine has coil-on-plugs. these may still be good enough because you did not report a misfire code.
I hope you kept up with the oil changes, and transmission service (if it's automatic). If it is a manual you should consider fresh transmission oil.

Manual or not: your car is due for a coolant flush.

Brake fluid should be replaced every 2 to 3 years.