Losing revs and cutting out even when idling and engine is rev'd

Does it have fresh gas ? Did you run out old gas , if you let gas in for a time it will varnish up , clog fuel system . It will have a funny smell to it .

Check to see if it has a Throttle positioning sensor. A faulty one will cause the engine not to run properly. It will do like you described with the engine revving and then wanting to cut out.

Sounds like you have a fuel issue. It could be a fuel pump cutting in and out. It could be fuel pressure regulator, or an injector not spraying correct. I think it's time to find an honest educated repairman.

Have you even considered the heater core? Have the heater core checked/replaced. As for the top hose collapsing...that is not good. Have the entire system checked out by a qualified mechanic.

chech fuel pressure possible fuel pump giving up try to chande fuel filter and see if helps

SCAN IT AND CHECK THE IDLE SPEED CONTROL.SOUND LIKE IDLE SPEED CONTROL IS FAULTY.

Revs.
As for the issue of the idle revs, that's perfectly normal. When it's cold outside, every car is supposed to have a higher rev in order to warm up the engine quickly. In more advanced cars, the computer wont even allow the engine to shift into overdrive when it's cold outside in order to avoid extreme engine stress and damage. When it's warm outside, the engine doesn't need to idle high because the engine is already at a good operating temperature. Not much will be needed to get it to the right temperature.
Intermittent Jerking

There is a long list of things that could cause intermittent jerking. I'm going to name all of them for you, but your best best would be to go to a mechanic and have them do an inspection.
Clogged PCV Valve (Possibly if you don't get your oil changes on time, sign of a tune up)
Bad DIstributor Cap (not likely at 140,000 miles)
Clogged fuel filter (Very likely, usually done with tune up)
Bad Fuel Pump (Not so likely)
Defective ECM (also not likely)
Vacuum hoses/leak (not likely but possible)
MAS (Mass Airflow Sensor--not likely but possible)
Fuel INjectors (if so, sign of a needed tune up)
Faulty Spark Plug Wires (not likely if tune up is recent)
Faulty O2 Sensors (possibly)

Clogged Catalytic Converter (Possible)
~Hope this helps

its most likly to be the idle control valve that just needs cleaning out but only use petrol as carb cleaner can destroy the seals

sounds like the idle speed sensor,if your rpm's are idling up and down

Quick and easy attempt to fix might be to try some fuel injector cleaner,the purple bottle stuff I put in, is only about $3 a bottle, and seems to eliminate similiar symptoms brought on by bad gas.