As others have said you are nose high on the trailer and have too much squat on the truck. The problem is I don't think you can go any lower on your drop shank. They gave you too short of a drop to get the tt level (you want to be level or slightly nose down, never nose high). Next you need to transfer more weight to the front of the truck. This thread
might help you better understand how to fix this issue.
In terms of loading stuff in the truck. As long as you aren't overloaded on payload you should be fine. We used to put bikes in the bed of the truck all the time when we had a tt. There are two camps on putting bikes on the rear of the tt. Some say no problem, others will tell you your bumper will fail and the bikes will be lost. We chose not to take the chance.
Once you get our hitch dialed in better you can decide whether or not you need to add an additional friction sway bar or two.