Thats crap, how dealers easily wash off hands here with their warranty by saying its normal. Why dont you ask any specialized gear mecahnics shop like AC Delco, ZF in aweer area check the car and give you in writing whats wrong with gear. Once you have this report show it to dealer and ask them to fix under warranty. This is absolutely not a normal behavior and it def sounds like a gear misbehavior due to something.
For point number 3, try to warm up car nicely from idle for like 10-15 mins and then drive and see if it still shakes. If it doesnt may be the oil reaching the AT taking some time, and once car is fully warm it circulate better.