I would start with compression test, compression is mechanical so is either good or isn't, can't be intermittent.
Prior to compression test you can also do a Glove Test to see if head is cracked or head gasket is blown, the white smoke.
I assume cooling system is in tact, it needs to be for this test.
Pull off rad cap and pull off overflow hose
Plug overflow hose opening
Put latex glove over rad cap opening and seal it with rubber band, you can use a balloon or even a condom instead of glove.
Unplug Coil Packs, you want a no start, or pull Fuel Pump relay
Crank engine and watch the glove
If it bounces then there is a cylinder leak, head gasket or cracked head
If it just lays there then you don't.
If glove bounces then you can find out which cylinder(s) have the leak.
Pull out 1 spark plug at a time and crank engine
When the glove stops bouncing last spark plug pulled was from the leaking cylinder, put it back in to confirm.
Broken timing belt wouldn't cause problems within the engine.
Lima engine, 2.3l/2.5l, are non-interference engines, this means pistons and valves do not share any space in the cylinders, so wide open valve and piston at top dead center wouldn't touch.
The rough running and "white smoke" wouldn't be cause by broken timing belt
Broken water pump belt YES, overheating causes the other issues mentioned above.
Last edited by RonD; 05-31-2016 at 08:35 PM.