Before condemming booster, replace check [ plastic ] valve. A good test for booster is With motor off, pump brakes many times to bleed off vacuum, while holding down brake pedal, start engine, pedal should drop to floor, if it doesn't booster isn't working. Some cars had adjustable pushrods, master pushrod could be " short "
Your sway could be anything, start with a good alignment. How to front tires look ? Most tire shops have a chart that shows what front end problems look like. I'd suspect tie rod ends.