Super stiff suspension

Unfortunately they are known for it. We see once a week here! Lots of help online

https://www.google.com/search?q=1996+Lincoln+Town+car+rear+air+suspension+issue

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If there is no noise when driving the car over a flat bump-free surface, it tends to suggest that the problem may well lie in the shock absorber or spring .. or .. as someone else has pointed out .. the bushes. A worn rubber bush permits metal to etal contact - the tapping noise .. and can also cause vibration.

Pushing down on the corner of your car should feel stiff as you are pushing against the shock absorber. If the spring is broken your car well make a heavy 'crashing noise' over each bump. Though any rubberised bush that is worn can also cause the same sound when driven over a bump.

If the car makes that tapping noise even when driven over an even surface it cold point to bearing troubles. However, as you say that it is bone jarring when up to speed suggests the problem lies in either a loose wheel nut, an out of balance or damaged wheel rim or worn rubber bush - or something worn that allows metal to metal contact.

The easiest solution - and the cheapest - is to take your car to a workshop. They will tell you within minutes what the problem is. If you try and replace parts yourself to cure the problem .. well .. usually we replace the wrong part and end up paying more for parts before we find the problem. The other point to bear in mind is that it isn't always easy to identify something like a worn rubber bush when the car is standing on the ground. It's easier when it has it has the weight lifted from its wheels - on a hoist.

Get your car to a workshop and let them identify the fault. You can change the worn parts yourself

It is hard to tell with out more detail as to what makes it squeak. Does it squeak when you hit a bump, or while the vehicle is in motion? To test your struts simply push down on each front corner (above or next to headlight)as to rock the vehicle up and down. Pick a solid part as to not dent it. This is a good way to test your struts. If it goes up in a stiff motion(not rocking) its probably good. If it goes up and down easily and has a lot of play then your struts might need changes. The squeak could also be sway bar bushings as well. If it only squeaks when your in motion it could be your cv axle. If you are still in need please post more detail as to better diagnose the issue.

need a little more detail here.
Rumble from front? rear? left or right side?
And shake in the steering wheel?
How big a bump and how fast were you going?
Was the rumble instant after the bump?
Is it constantly making the noise or now and again?

Look at the rear suspension. I think it is one leaf spring upside down over top of the axel. At the ends they are grinding in there seats. Jack the vehicle up by the body clean out the spring seats and oil them a little its just showing its age.

Several possibilities, You could have worn out brake pads or a brake pad scratcher telling you it is time. You could have bad wheel bearings. If you back into parking spaces till you bump the curb, you could have broken or bent suspension bushings. Could just be one dry shock absorber. Could be an automatic brake adjuster that is set too tight causing brake pad glazing/squeaking. If it happens when you bounce it is suspension. If it happens when you roll its Brake/bearing.

How do you know it's a sensor problem ? DTC - diagnostic trouble code ? Take's professional type scanner to read these DTC'S
DTC B0958 01: Parking Aid Rear Sensor 1 Left Corner Circuit Short to Battery
DTC B0958 06: Parking Aid Rear Sensor 1 Left Corner Circuit Short to Ground or Open
DTC B0958 08: Parking Aid Rear Sensor 1 Left Corner Circuit Signal Invalid
DTC B0958 21: Parking Aid Rear Sensor 1 Left Corner Circuit Incorrect Period
DTC B0959 01: Parking Aid Rear Sensor 1 Left Middle Circuit Short to Battery
DTC B0959 06: Parking Aid Rear Sensor 1 Left Middle Circuit Short to Ground or Open
DTC B0959 08: Parking Aid Rear Sensor 1 Left Middle Circuit Signal Invalid
DTC B0959 21: Parking Aid Rear Sensor 1 Left Middle Circuit Incorrect Period

Could have other codes
DTC B0967 02: Parking Aid Switch Circuit Short to Ground
DTC B1008 42: Calibration Data Not Programmed
DTC B1E3A 03: Sensor Power Circuit Voltage Below Threshold
DTC B1E3A 07: Sensor Power Circuit Voltage Above Threshold

There are a lot of other qualified repair shop's besides the Dealer .

check stabilizer links and shock assorbers

There are a few suspension parts that can cause knocking noises. Such as swar bar loose, strut mounts going bad. You should really have a shop do a complete suspension check.

Sounds like your left front wheel bearing is going bad. When you make a right turn, or compress the right front suspension over a bump, it forces the car to roll to the left. This loads the suspension on the left side, which will exaggerate a wheel bearing problem. Are you hearing the noise at all when travelling on the highway in a straight line? If so, it'd be either a grinding sound or a hollow humming noise. If you aren't, it may be that the bearing is just starting to go bad.

A quick test to see if the bearing is bad is to jack the car up at that corner, grab the wheel at the top and bottom, and shake it hard - if there is any movement or looseness, your bearing is shot. If there is none, it doesn't mean the bearing is fine, but it could be that it's just starting to go bad (which would be why you only hear it in turns and bumps, but not straight-line yet).