Some of these have already been covered, but the first one, not yet.
Assuming you are on P-Rated tires, inflate them to the max pressure loaded (see sidewall). This will help remove some squishiness.
Your dealer set up the hitch. First thing you need to do is go to the post provided, dismantle your dealer set up and set up from scratch. In general, dealers are pretty much worthless in this aspect.
You have 7400# dry trailer, it is at least 8,400# and probably heavier loaded. At that, you are too heavy for a half ton (I'm talking comfort, not weight abilities). We experienced this with our first trailer. Took a $10k bath after one year to move to a more comfortable trailer (6,000# dry - 7,200# wet).
We have a standard round-bar WDH with friction sway bars. Our set up came with one sway bar and we towed like that for about 3 years. Puckered every time a big rig would pass us and had to slow considerably when driving with a crosswind. Added a second sway bar a couple of years ago. Night and Day.
But bottom line is, 8,000# plus is too heavy for half ton comfort, regardless if you are within limits of the TV or not (probably not).
Need to weigh your rig to determine actual weight. The only thing a dry weight is good for is to get you in the neighborhood. We add about 1200# of gear to our empty trailer.