If you have identical twins, will they both develop the same genetic/inherited disease at the same point?

Depends: If it's something that fully expresses itself with no modification (such as huntington's), yes. If it's going to express itself but is lifestyle-modifiable (type ii diabetes), timing will differ. The diseases for which there's a genetic component (diabetes, lupus, multiple sclerosis, many others) have only one twin affected more often than not -- you can find details.