Your new baby is still a very low mileage car for its age.
I would tackle the different problems you are having by starting with the most important i.e.: Safety
handling: The loose feeling you are reporting could be caused by several different elements:1) Tires in good condition???? Check tiree pressure and bring it up to spec..
2) Have the shock absorbers tested, also have a look at the front strut mounts.
3) Rear suspension arms: rubber bushing tend to degrade with age.
4) Check all steering linkage for play and rubber bushing for deterioration, including ball joints. Everything should be tight.
Frame mounts (differential) should also be looked at.
Tranny:
Your tranny does not start in first gear, but in second gear so you will normally only feel 2 shifts (2nd to 3rd, and 3rd to 4th)

Sorry, can't help for the 2 other problems.