Rough idle and smooth idle

Dirt coming from the exhause openings - what exhaust openings?

You are obviously loosing coolant from the cooling system. Any water or coolant in the oil?

I suggest a compression check. Determine if the cylinder compression is weak and check to see if the compression is consistant in all cylinders.

After that it is time to get down and dirty. I would pull off the head, have it looked at and checked for cracks and warpage. I would look at the head gasket to see if it is bad and note what the top of the pistons look like. Are they oilly, does it appear that the oil is coming from the rings or dripping down through the head. The engine is not good. Head gasket and head check could fix it or improve it. But if the rings are bad it is engine rebuild or replacement time.

A few things to check would be are:

Start spark and proper fuel pressure.

Fuel pressure should be at 36-38psi and spike 10psi when there is no vacuum.

The spark when tested should be bright and a blue/white spark.

These tests should be done when the vehicle is warm and is acting up.

The idle is still going up and down? If it occurs all the time, look at the hoses for a vac leak. The intake manifold and manifold gasket could be leaking. Don't discount this. Had any work done around this area? The air could be getting into the intake manifold unregulated and confuse the computer thus causing the surging of the engine.