If you can only get the car to move forward from a stop by pulling the shifter into manual 2nd or 1st then you likely have a broken forward apply band, but because of your other symptoms there is likely more going on. A broken forward apply band will give you no movement from a stop in D or 3 range, but in manual 2 and 1 there is another band that applies for engine braking purposes but is just enough holding power to get the car moving and then you can manually upshift and if it never falls below 2nd gear it will hold just fine. When you got on the gas a bit and it felt like it was in neutral this may have been the start of your problems. I would see if you have any apply at all after the car cools down and see if it will pull at all from a stop in D or 3 and if not it requires internal repair as the forward apply band is literally the second to last part that comes out of the case on a teardown so you are looking at a complete rebuild to fix the problem. IF you do have some movement from a stop after the trans has cooled off then you likely have a badly worn input clutch apply piston which can also cause this and by pulling the shifter into manual 1st the line pressure is much higher and can overcome the wear and get the car moving. Either way these are both internal problems and since you mention your fluid level being ok then that isnt causing your problems. The rough idle at a stop is odd also and I would check for maf codes to make sure it isnt going bad which will cause it to run rough and also cause low line pressure if the signal drops out or is very low.
