Desktop Power Supply – Is Grounding Necessary?

You wouldn't experience any problems except in the rare case that your laptop has an internal short from a live power line conductor to an exposed metal part of the laptop.

The ground plug is purely for safety and has no effect on the proper operation of an electrical appliance. It accomplishes two things. First, it assures that the plug is inserted with the proper orientation so that the hot wire of the socket is connected in a predictable way to the appliance. Second, the safety ground wire is typically used in appliances that have a conductive case and the case is connected to the safety ground. If a short circuit were to occur inside the appliance, any current will be passed through ground, rather than through the body of someone who touches the conductive case.

The laptop will work just fine if the ground plug is removed or if the hot wire and neutral wire are reversed.

To answer the title of you're question, you may not want to remove the grounding pin because "If the customer alters the product in any way, then all warantees are void. It is, by definition, the customer's fault, whether there are technical reasons or not."

Question 1: Yes, you can because after all it's the PC's power supply. Its output voltage on the 4-pin molex connector is the same as the external power adapter.

Question 3: And of-course you can connect that many HDDs, that you have ports on the supply.

Question 2: It's totally safe if the power supply is working correctly.

But the problem is it turns on only when it is connected to a PC, but the hack is you have to connect the green wire coming out from the supply to the any black ground wire.

See How to Power Up an ATX Power Supply Without a PC!.