Hi and hope you get your issues resolved. From your description you definitely have suspension issues with that truck. You need to get that fixed by a compentant shop. Your second problem is under rated tires for that trucks suspension and wieght. Although D rated tires might be ok for that size trailer but you definitely need to be running those tires at maximum side wall pressure. Better yet go get OEM sized tires as identified on your door sticker (they are probably 235/85/R16 or R17 E rated)
Your WDH needs to be tightened just a little although an F350 should be able to tow that wieght trailer without any WDH at all with no problem. Get your suspension fixed and then go from there.
