Having engine misfire problems?

My car jerks when I put it into gears and my low coolant light is on, but the coolant part is full and sometimes it shakes when I am driving.

I have an 02 Sable Duractach 3.0 V6 that is misfiring. Seems to be worse when the vehicle is first driven and seems to go away quite a bit after usual city driving. However if AC comes on it will misfire occasionally while driving and will misfire quite a bit if stopped in traffic. The mechanic who I've never used before says he needs to do a compression test and that it will be $220 to have the test done. My question is wether or not this is worth it. I just want to make sure I'm not being had. I really do think its the coil pack or injection coil, is there an easy way he can check to see if these are bad before doing the compression test? Or if I pay for the compression test will it also let the mechanic know that the coil pack or injection coil is bad? Also the only other code that is showing on diag is b-1600 (Pass antitheft tran) pretty sure thats totally unrelated but just throwing it out there.

Replaced plugs, wires and coil. Problem remains.

I have a 3.0 dohc that is misfireing, 1st time I checked it was in cylinder #1 then it went to cylinder #6. I have put in a new egr vaule, vgr vaule sensor, coil pack, cranshift sensor, new spark pulgs and wires, new manifold seals, new #6 fuel injector and still have a misfire on #6? It stalls sometimes when I stop, and idols below 500 when in drive and around 700 in park. Auto zone troubleshooting code is p0316 & p0306 and at one point in time code p0301 but that one comes and goes the 1st time that I check it was there 2nd time I check it was not 3rd time I check it was there and now that code is not showing up but I have unpluged the battery so it may be that it just reset the computer and its been there along? Code p0306 has been there every time which is a misfire in #6 cyl. It also has made a backfire sound but not everytime but have heard 4-5 times. It also pops when I take off?

I will get a compression check tomorrow, got new plugs and wires got a new coil and got good spark, new egr vaule but there dont seem to be much suckage on the hose that connects to the top of the egr vaule? Should there be alot of suckage in that hose? But I still need to check the oxygen sensor.I had it at bennett fords and they said it was the #6 fuel injector but I put a new one in and still running rough. O yeah plus when I took it back to auto zone it still had the p0306 code plus a new code saying my fuel prussure is low. When I turn on the a/c its even worst could that just be from the extra prussure on the engine with the misfireing
cyl(s)?

Compression check completed today and everything was fine there Changed Air temp sensor and she is now purring like a kitten, so everyone better look out cause I am back on the road again lol

Engine light on, replace bad spark plugs still misfires. There is some kind of air leak sound in back right side of manifold, makes a sucking sound when I give it gas, checked for vaccum leaks cant find any, could coil pack make this sound or

Own 2003 mercury sable gs, 116K, 3.0L, V6, SFI. Veh misfires on cyl #2. Had veh to ford, mercury and private tech. Things done: replaced plug/wire, checked coil, relative comp check, injector flow test, power bal test, changed out cyl 2 injector, comp check 160, motor vac and injector service, ran techron through gas tank, ran 2 cycle oil 8oz through gas tank. Check engine light still comes on with misfire code and when starting up cold engine has real slight shake, but warms up runs smooth. Spend over $300 and car not repaired. Do you experts think taking head off last resort and/or is there other test to try? I was thinking of leakdown.