2020 Hyundai Santa FE drivetrain & axles problems

When stopped at a traffic light and the auto engine turn off kicks in as expected with my foot on the brake pedal. However, the behavior is very erratic when I release my foot from the brake. Sometimes the vehicle jumps aggressively without me applying any acceleration and sometimes the engine just starts and the vehicle does not move until I apply some acceleration. I almost rear ended the cars infront of me few times. I got way too skeptical and began turning off the auto turn off feature when I get into my car.

There are three issues: 1.) in sport mode, the transmission will sometimes get stuck/hung in gear (maybe gear 3 or gear4) and will not shift into the next gear, even when increasing speed. 2.) also in sport mode, after driving for about 10 or 15 minutes the transmission will often slip into gear 5, after revving high and can be heard revving, but it is not reflected on the tachometer, and then when the gear catches it is a violet jerk forward.