Nissan: coolant and start problems with 2002 sentra GXE, dual overhead cam, nissan sentra


Question
I bought this 2002 Nissan sentra GXE used in fall of 2004.  1.8L dual overhead cam, automatic.  It has had issues however with the cooling system, and intermittent rough idle on first starting it.  
first, the cooling system issue:
The car started overheating and even got to the point where the engine started to cut out (internal computer telling it to shut down I think).  I brought it into the mechanic and they thought it was the thermostat (likely considering the symptoms)  so they replaced the thermostat and it seemed to be fine.  I drove it home and on our way out of town it overheated again.  we brought it right back to the shop.  they changed the radiator cap and the water pump pulley and called it good.  we didn't have problems for some time, and then when winter rolled around, the heat wasn't working very well if at all.  so we brought it to a different mechanic and they said it was likely the thermostat, I told them it had recently been replaced and they recommended that it needed an OEM thermostat.  When they got into it they said that the radiator was not allowing enough flow through it and that it should be replaced (I said ok hoping it would fix the problem and I wouldn't have to deal with it again, although it seemed unlikely to me that the radiator was bad).  so after these two things were done it seemed to run fine for some time.  It is now starting to overheat again and the heat is still not very good, seems to only output when driving.  when the car is idling the air coming out is cool to lukewarm.  Also, during the winter I would occasionally hear what sounded like trickling water rolling across behind the dashboard, especially on sharp turns.  I don't have any idea where this sound is coming from, but I suspect the thermostat is bad again-causing the poor heating.  Is this likely?  it's been replaced at least twice (I've lost count now) within the last year.

now the rough idle issue (same car):
the car started to have a rough idle about the same time as the radiator problem, at first I thought it was a transmission problem since it seemed like the car was trying to go while it was in park.  then it seemed to be more likely that it was a rough idle and would smooth out as the car warmed up.  at the same time as the occurence of the rough idle, the check engine light came on and the code said there was some misfire occuring in the number 3 cylinder and that damage might occur to the catalytic converter due to un-burnt fuel contacting the catalyst.  the recommended fix was to check/replace the spark plugs and the coil for the #3 cylinder.  I did this and still have the problem with the same code and cylinder.  another mechanic recommended I run a fuel cleaner through it and give it a tank of premium fuel.  this seems to have helped, but still have rough idle occasionally and the check engine light has come on intermittently with the same error code.  
I also had a cold start problem, but replacing the recalled sensors (crank, ignition, and timing I think?) seems to have fixed that problem.

Any suggestions on how to resolve these issues?  I've seen internet posts by other nissan owners with similar issues. Thanks for your help!


Answer
Yeah, you have engine failure. You are getting combustion pressure in your cooling system at the cylinder head or its gasket. This is displacing your coolant and causing your problems. You may also have damage to sensors if you overheated the car that bad. Two good bits of advice: Never run and engine hot!! Never run and engine low on oil.