Q: Hesitation

Vehicle just recently started hesitating under hard acceleration, and is very bad especially from a stop, it sometimes is so bad where the vehicle feels as if it wanted to stall, I recently cleaned the mass air flow sensor and also got a new air filter and also cleaned the throttle body. I did try and research the issue and came across the EGR valve which I did notice on my vehicle is very old and rusted. I was driving the vehicle today and was cruising and tried to accelerate hard and the car seemed confused on what to do , or how much air it needed , and also when trying to accelerate hard you could hear like a thumping sound , not really sure where it came from but this issue is very annoying and i would love to be helped and get this issue resolved, and the vehicle starts fine and idles okay , I wouldn't really say it has a rough idle. And the vehicle also hesitstes when pressing on the gas pedal while car is idling in park

My car has 127000 miles.
My car has an automatic transmission. 2002 mustang 3.8l v6