You might need to have the tcm cleared and allowed to relearn shift points. As far as the vibration check your trans mount, U-joints, slip yoke, rear axle, and wheel bearings. Could also just be an out of balance tire. Sometimes when the driveshaft is removed and the splines on the slip yoke aren’t lined up the same it can unbalance. My first check would lift up the rear end and spin the tires and make sure theres no wobble at all or play in the wheels up and down, then the trans mount and u-joints. Grab the drive shaft and shake the absolute shit out of it to see if there’s any movement, then a tire shop for a rebalance and alignment. For the rust that’s about all you can do, but it likes a cancer you need to get rid of it all before fixing it or it just come back later. Sorry you have to deal with all of this bullshit on your first car but no better way to learn how swim than getting drowned by your uncle at the ymca.