Mass Air Flow Sensor????????
Now that I read all of the problems again this sounds like all of the symptoms.
It does happen once the car is warm and it almost feels like a trans slip. Idle is fine most of the time, harder acceleration like in 2,3,4th gears is when it happens.
The sensor tricks the brain and it thinks its getting to much air to fuel ratio so it cuts the air and it feels like the car wants to die.
You can try to clean it, or test the wires, but I think its best to replace it.
It is the compnent right next to the air filter, very easy to replace and just takes a few minutes. Un-do the two screws and disconnect the wire harness. (ps. might want to disconnect the battery) and Cost $85 and usually a core exchange of $50
Hope this helps. GOOD LUCK