1.beijing airport: show passport and original AP
2. US: fill out new I-94. the IO at NY JFK did mention to me no I-94 necessary, however he still attached the departure portion to my passport. so no harm doing it.
3. don't know about Chicago, but at JFK, there is a office for AP and others.
4. only passport and AP approval notice are needed. they don't care about the receipt.