Some of it ... the steering wheel still has some slop/play/loose. I'm betting it's going to need a new rack. Power steering is great for a parking lot - but sucks at speed .. and it's a Ford - so it has a leak. I did get to inspect the entire front end while it was up on the lift at the tire shop. Appears the front sway bar hardware is old and worn and the shocks are pretty old - bushing at mounts are cracked/worn in them too. All getting replaced.
Your car doesn't have a rack, it has a steering box, and a hydraulic cylinder for power assist. Check your inner and outer tie rod ends. Look at the idler arm, and bracket. Check for cracks in the shock towers, check the strut rod bushings, etc. You'll find something that's not right, or a combination of a bunch of little things. Mustangs weren't built as road racers, the front end came from an econobox Falcon. That's not to say you can't make them handle well without spending bunches of bucks on a new aftermarket front end. I've done them both ways and a rebuilt, properly aligned stock frontend is plenty stable at speed with power assist. Unless you are going autocrossing, or road racing it won't be a problem.
As far as leaks go, it's almost always the power cylinder or the control valve, providing the fittings and hoses are good.
The cool thing about Mustangs is parts are readily available and cheap compared to other marks. If you do the work yourself you won't have 1500 bucks in a complete rebuild, from box to ball joints, and a modern alignment.
Have fun with your new toy.