A couple of things are likely;
If you are running OT exhaust with a high overlap cam, shortly after decelleration, you get reversion, you pull a small amount of water into your cumbustion chamber, hence the roughened idle. This cools your exhaust valves to rapidly, into a martinistic state, and over a period of time the valve crystalizes, and can no longer take the constant slamming into the seat. It fatigues, and breaks off.
You could be running older heads, that are not designed to run on unleaded fuel. The exhaust stem has no lubrication, it expands, friction increases in the guide, the friction overcomes the springs ability to pull the valve back into position, and the piston hits the valve, bending it over, and the second hit breaks it off.
You could have weak valve springs. The bent push rod tells of a severe mechanical interference, so when the piston was coming up, the valve was attempting to open. I'd say the problem is in the guide interference from your description.
The water in the oil can be explained from the compromise in the integrety of either a cylinder wall, or head. Look around the forensics of failure analysis is exciting, and will make you a more informed hot rodder!