What could be the cause of my car's vibration/shakes.

There are a few posibilities;

One of the more common problems is failed motor mounts. Motor mounts have rubber inserts that dampen vibration and after time they become brittle and fail from common wear and tear. With the mileage on your car, this is a good posibility.

Then there is your common tuning problems. If one cylinder is not performaing like the others, the engine will vibrate. The reasons a cylinder can be weak are compression, a bad fuel injector, or even a head gasket leak.
Sometimes times flywheel or balnce wheel can get out of whack due to stretching of the timing chain or a worn sprocket can throw the timing off enough to casue a poor idle. It can aslo casue detenation and damage to the engine. Again with the mileage on your car a timing chain would be in orderas regular maintenance. Consult your owners' manual or a dealership for exact mileage suggested to replace it.

So, you can do a test to check your motor mounts. Is a little crude but it can at least give you an idea if that is the issue.
With the engine running and the hood open, put the car in drive and put the parking brake on. Also put the brake pedal down to ensure the car does not move. Give the car a blip of the throttle and watch the engine for movement when you do so. If it moves more than an inch or so and then seems to fall back into place without any cushioning or it makes a noise when it drops back down, the motor mounts all need to be replaced at one time. The reason they all are replaced at once is that if you replace one, the others are not in good shape at their age and will have an increase in load on them. This will make them fail rather quickly. When they fail the load is then transfered to your newest motor mount and it could fail quickly as well. You also want to replace the transmission mounts with them. It sounds like a lot but the other issue is that the engine is not sitting where it is suppose to and that along with the excess movement can damage other componetns.

As far as the engine performance. If the mounts are okay. Check the cylinder compression first to check for a bad cylinder.

If you have any other questions, please come back and we will be haere.

It is hard to say exactly what damage you are doing to your car, IF, it is the motor mounts. Failed motor mounts usually allow an extra 3-5" of engine travel. While most of the hoses, cables and wires have some slack for engine movement, they could get pinched or rub up against something repeatedly enough to wear off the insulation.
The biggest factor that is hard to determine is that engine and transmission alignment in relation to the sub frame and other components is imports. Angles as well as distance and sometimes motors will sit unevenly. This wears out components like axles, it can wear the brackets that hold your motor mounts and I have seen in extreme cases where the engine was sitting on the sub frame and the angle damaged the block.

So, I can't tell you exactly what is happening, only give you an idea of the importance of proper engine alignment and vibration/isolation is to many large components.

So, driving the car easier will help. When you hit potholes it hurts and all you can do is purchase the mounts and replace them.

It is generally not hard to do. I tried to find the location of the motor mounts, but they are generally in common places;
On transverse or sideways mounted engines;
There is a mount on the lower front
There is a mount on both ends
There is a mount on the rear which attaches to the sub frame
There is a mount on the transmission either on top or the back or front of the transmission. This one you have to hunt down. If you buy the mounts you can usually find them by looking at the new ones and looking for the like part.

On in-line mounted engines;

There is a mount on both sides
There is a transmission mount on the rear cross member that supports the rear of the transmission

While I was looking for this information, Ford did have a note in bold letters saying, "The driveline angle of the drive shaft is critical to components prematurely wearing and getting damaged. This is especially true of universal joints." I am assuming you have an in-line ounted engine, where the accessories are in the front of the motor. This will also put strain on the differentials.

So, it is important to replace them all ASAP.
Look on-line for the best deals. Try thefind. Com, but beware of web sites that are, "thrown together" and unprofessional looking with prices to good to be true. Expect to pay around $50 per mount give or take $20. If you have an in-line motor you only need 3 and transverse require 5, but are cheaper. Rockauto. Com is a good place for closeout sales and usautoparts. Com is also good.

Gets those mounts replaced because $200.00 in maintenance will save $2000.00 in repair.

That may be the balance shaft on the motor.
There are two gears to this part. One is directly behind the upper timing chain gear. The other is just above that. If they are worn, this can cause a vibration. It throws the timing off and that may rock left to right as the engine.
With the mileage on your car, it is about time to replace the timing chain. This would make it easy to replace the balance shaft assenmley at the same time.
The only other thing I can think of is a bad cylinder.

To check the compression crank the engine over at least 5 and record the highest reading. Repeat the procedure for all cylinders using aproximately the same number of revolutions. The lowest compression should not be less than 75% of the highest compression reading.
Compression should not be below 100 PSI.
You can usually borrow or rent a compresion test gauge at an Advance auto or auto parts store. It will have adapters to fit the sprak plug holes on your engine.

That about covers it.
Take care.

Dr.C