Yes, the pushrod went through the oil hole and is now in the crankcase. you will probably have to open it up to get it out and it is probably bent as well.
The best way to fix the valve guide in the head is to replace it.
You have an overheating problem too. Either the fins on the block and head were stopped up the fins are gone off the flywheel fan, or the engine was running too lean and a carb. cleaning is in order.