If your AFM is shot - it wont accelerate like it should, the item what you are calling fuel filter is the fuel pump strainer only, the actual fuel filter is in the engine room, follow the high pressure fuel pipe from the fuel rail and you will find it, If the car was standing for over a few years its best to change it out now.
to inspect the AFM very carefully remove the top plastic cover from it (the piece which says nippon denso) use a blade on its edges to pop it out, it will take a while. Then check the carbon tracks with a magnifying glass to see if they are worn, DO NOT apply anything like carb cleaner in there and DO NOT unload the spring unless you know how to put it back exactly as it was.
To test the engine - try to move the AFM gate with a wire as the engine idles and see what happens.
btw - do you have your check engine light working?