Can one use all the olive oils for cooking ?
The short answer is yes you can but there are things to consider.
You can cook with olive oil but it has a heavy flavor and a lower smoking point than a lot of the oils you can cook with (such as peanut oil which has the highest smoke point of the cooking oils) which causes it to heavily flavor (and sometimes overpower) whatever it is you are cooking. The low smoking point also requires food be cooked slower which causes food to absorb oil.
Extra virgin olive oil should be used sparingly and in conjunction with a secondary, lighter, oil to allow you to cook at a higher temperature and with a less heavy flavor being imparted to the food.
Less is more is a good adage when cooking with olive oils.