I am already crazy, so I will just answer one.

If the transmission mount is original, you can bet that it could stand to be renewed, along with the engine mounts. The transmission mount is easy to replace. Having a small jack helps. (Otherwise, you can let air out of the tires, a trick I learned here at the asylum. They don't like us to have tools here.) The motor mounts are somewhat challenging because of access problems. But rewarding, nontheless. Your vibration could be due to a worn driveshaft center support and/or bearing. If you change those, consider renewing the flex disks at the same time. ("Renew" is a Mercedes term. On a Ford, parts are replaced. On a Mercedes, they are renewed.)

Caulking the axle boots? Well, at least the previous owner was an optimist.