Valves usually only g et smashed when an interference type engine throws it's timing belt. It would be a good idea to do a decent lap job and new seals if you purchased a used head.

A1: Thermostat and cooling system maintenance will prolong overheating/cracking. Either way, these things get old - they crack. It happens.

A2: Oil is supplied by the pump. The pump can not lubricate unless it is turning. In short - replace the head, fire it up.

A3: Replace the thermostat, inspect the radiator fins for damage (resulting in low flow), inspect for significant blockage I'm head and block (rust and buildup), replace the thermostat, add fresh coolant. A fan shroud will help cooling, but it will survive without.