What is a cylinder compression how much do it cost to replace it

Not a problem I have heard about and certainly isn't something Ford products are prone to.

I certainly wouldn't land my customer a bill for a replacement engine on the strength of a compression test. The compression test is a notoriously unreliable method of assessing engine condition and is useful only as a quick and simple check to discover whether further investigation of compression-related components are needed or whether something else is causing the trouble.

In the case of low compression a cylinder leakage test should be carried out in order to pinpoint where the compression is escaping and then armed with that information the repairer should offer the option of repair, the fitting of an exchange cylinder head, the fitting of a short engine, a conditioned or a reconditioned engine and explain the relative costs and advantages of each option.

It is worth noting a condition called tappet jacking can cause a loss of compression and several times I have encountered Ford engines that have suddenly shed carbon from the piston tops which has become trapped under the valve seats causing such a massive loss of compression the engines stopped. The first time I removed the cylinder head but subsequently I poured Red-X upper cylinder lubricant into the cylinders and eventually they restarted and after a few minutes once again ran normally.
One of those vehicles was a taxi and the carbon shedding happened every 40,000 miles...

What is the compression on the other cylinders, 110 lbs is low, however it is suffeint to fire so if the plug,coil and injector are working it should fire that cylinder

There is always a better alternative than the dealership as far as costs. They want to put a new motor in a 2003 model? That is ridiculous to me- cost-prohibitive. Find a reputable independent shop. Look for references and customer satisfaction. A used, low mileage replacement engine is a better alternative, probably less than half the cost of a new engine.
There may be an even better alternative, where you refurbish the top end of the engine-the cylinder head and valve train. This is dependent on that a wet-dry compression test supports rebuilding the top end. What I mean by this is a compression test of the cylinders reveals low compression in one or more cylinders, okay. Next, they would squirt some oil (about a tablespoon) in the low cylinders and check compression again. If compression doesn't change, it points to the valves and valve train (the valve guides which wear and could let oil into the cylinder). But if compression is higher in the wet test, then the piston rings are worn and losing compression, and oil gets past them-this would indicate the engine needs a complete rebuild or a replacement is called for. The reason for the wet test is that the oil will temporarily seal around the piston rings and improve compression if the rings are the problem.
If the test shows the valves are the problem (and it is very possible on an engine with only 120K-your bottom end could be fine), then a top end rebuild of the engine is a much cheaper route than any other choices. You may not know this, but often a little oil burning in the cylinders at start-up is nothing more than the valve stem rubber seals are deteriorated-a real cheap fix. The dealership probably won't tell you this. However, with the loss of power, well, that points to something more severe than valve stem seals. So I would recommend the wet compression test, just to check if it is the top end or the bottom end. If it's the top end, you could have the cylinder head reconditioned and motor along for a few more years, trouble free.
Similar to a compression test, a "leak down" test of the cylinders is actually a more accurate method of finding where compression is lost, and it's only a one step test. They hold compressed air in the cylinder and analyze where it escapes to pinpoint compression loss. Loss of compression translates into loss of power. Have either test done before you decide. Find a good mechanic and trust his advice. (Stay far away from dealers. Greed is their motivating factor.)

Blue smoke indicates burning oil in the cylinders. Could be worn piston rings, worn valve guides, or bad valve stem seals. An engine compression test may help find it, but a cylinder leak-down test is a more precise way to find where compression is being lost. If compression is good, you just may need to replace the old rubber valve stem seals. A shop could do it without having to remove the cylinder head, using an air compressor hooked up into each cylinder while the valve train is being worked on. The air is used to keep the valves from falling into the cylinder while the seals are replaced. About a 4 hour labor cost, so expensive, but a lot less than a cylinder head removal.

IF YOU HAVE CYLINDER HEAD DAMAGE MORE LIKELY PISTONS HEADS DAMAGED ALSO. PROBABLY END UP BUYING REBUILT ENGINE.IF YOU BUY NEW CYLINDER HEAD, STILL DONT WORK,THEN LABOR CHARGE ADD UP AGAIN REMOVE ENGINE CYLINDER HEAD WITH CYLINDER BLOCK.IF PISTON HEADS DAMAGED, BEST TO BUY REBUILT ENGINE.

No way to tell until someone identifies why the 3rd cylinder isn't working. It could be something as simple as plug wires or a coil pack. It could be a Crank Position sensor being faulty. You just won't know until you do some testing. Do a compression check and see if you have good compression and eliminate valve and ring problems. If the compression is good replace the plugs and wires and work your way through the system.

Replacing a cylinder head gasket is a miss or a hit. In some cases, just replacing the gasket may work. But if the cylinder head is bend, dealer may ask to replace it, because "machined aluminum heads rarely works". In this case the cost may be more than $1000. It is a good idea to send the cylinder head for inspection, in a machine shop. They charge $150 for inspecting, checking, cleaning and if necessary machining the head.
If the timing belt will be replaced this is an extra cost. If someone will just replace the gasket, on a bend cylinder head, it is more likely to blow out again. This problem can be solved if the gasket be replaced properly, checking and taking care for the cylinder head too.
As the coolant warms up, it expands and for that reason you have two marks at coolant bottle. Down cold and up hot. It is normal for the coolant to overflow from coolant bottle, if it is filled to the upper mark with engine cold, way up the cold coolant mark. Let engine to cool down overnight and set the level at coolant bottle at the lover mark cold. If it will overflow again this is a bad sign. The pressure at combustion chamber varies from 75 in idle up to 150 or more in higher RPM. If the cylinder head gasket is blown, then gases are blown into the cooling system, increasing the pressure, the radiator cap pressure relief valve is open and coolant is discharged in the coolant bottle. In such cases it is common for the coolant bottle to boil. You can observe gases discharging in the bottle, mixed with coolant, from the cooling system. These are symptoms of a blown cylinder head gasket. Because you replaced it once, there might be a bad (bend, deformed) CYLINDER HEAD too.
To find it out you have to perform cylinder compression test on your car (PROFESSIONALLY).
1. Start with a normal ("static") compression test. To eliminate rings, valves, holes in pistons, that sort of things. A normal cylinder balance test is also helpful (so you know which, if any, cylinder is presenting a problem). Engine should be warm.
2. Put all spark plugs but one back in. Ground that plug wire to prevent module damage. Disconnect that injector on a port fuel system.
3. Put your compression tester into the empty hole. The test can be done without a Shrader valve, but most people recommended leaving the valve in the gauge and "burping" the gauge every 5-6 "puffs".
4. Start the engine and take a reading. Write it down
5. Now goose the throttle for a "snap acceleration" reading. Reading should rise. Write it down NOTE: Don't use the gas pedal for this snap acceleration. The idea is to manually open then close throttle as fast as possible while without speeding up the engine. This forces the engine to take a "gulp" of air.
6. Now write down your readings for at least the bad cylinder (if there is a single bad cylinder) and maybe 2-3 good ones. Make a chart like this: CYL STATIC COMPR IDLE -RUNNING COMPR - SNAP Cyl 1 150 75 125 Cyl 2 175 80 130 Cyl 3 160 75 120 Cyl 4 160 80 125
7. ANALYSIS: Running compression at idle should be 50-75 psi (about half cranking compression). Snap throttle compression should be about 80% of cranking compression.
Consult a professional with the readings. If the gasket is to bad, you may have very low compression at lease in one cylinder.
If you will get a positive confirmation for a bad cylinder head then you have two options:
REBUILD THE CYLINDER HEAD or REPLACE IT.

i don't know how match the cost, but it will he you, first change the position of the ignition coil to another coil also the spark plug, read the misfire code is it P032 or replace the code, if on cylinder 2 again appear the misfire check the compression, if ok go to electrical and check wires go and from to cylinder two coil to pcm, check the ground on #2 coil, if all this ok, see the difference reading by multi tester to coil reference if all good, reprogram your pcm, or replace if necessary

sounds like a burnt valve or a flat camshaft or a broken rocker arm .is it a 6 cylinder or a 4 cylinder the cost will depend on that

Depends on your alarm system things could leed to that and it could also be something more costly like time for an engine overhaul cylinder head gascots burn with time and the cylinders loose compression to be sure have the compression check in the cylinders compare to OE standards tthat way you'll know what your dealing with