I would skip referring to "gigabytes" entirely:

How big a hard drive do you need?

And if you are a customer, you ask

What's the biggest drive on the market?

To my (AmE) ears, it seems odd to ask about the number of gigabytes; the thing I'm interested is the size of the drive, and I'd only talk about that until it comes time to specify a number.

Neither of your phrasings is acceptable, in my view. By analogy, if you were selling mugs, you would be saying, incorrectly:

1. What milliliter(s) mug do you need?
2. How many milliliters(s) mug do you need?

Correct wordings would include:

• What capacity mug do you need?
• What capacity mug do you need, in milliliters?
• How large of a mug do you need (in milliliters)?
• How many milliliters do you need for the capacity of your mug?

For hard disks, you could say any of the following:

• What capacity hard disk do you need?
• How large of a hard disk do you need, in gigabytes?
• How much disk space do you need?
• How many gigabytes of disk space do you need?

When comparing two hard disks, you would speak of…

• More/greater/higher/larger/bigger capacity
• More space
• More gigabytes

If you want to splurge, you would ask questions like:

• What is the largest hard disk available?
• Which is the largest hard disk you have in stock?

(It's generally assumed that when you say largest, you mean capacity, not physical dimensions.)

Since you were asked about a hard drive, there is no need to repeat it. I would just ask:

How many gigabytes/terabytes capacity do you need?

or just:

How much capacity do you need?

In your example;

2) How many gigabyte hard disk do you need?

I would interpret this to mean:

How many gigabyte hard disks do you need?

which is a different question. In this example, "gigabyte" is just a modifier of "hard disk".
However, this point might be opinion based.

Since I work with computers a lot, I know that there are plenty more things you could reasonably ask about a hard drive - and that counting gigabytes is a trifle unambitious in these times of multi-terabyte drives.

As other answers have noted, you should ask "how big" rather than "how many GB" or "what GB", though of those two, "how many gigabytes" is more correct. But what I would do instead is to produce a list (or display) of relevant products in stock, and invite the customer to choose between the possibilities.

Such a list is likely to contain external drives for the desktop or for portable use, internal mechanical drives in 3.5" size for desktop computers or 2.5" for laptops, and several ranges of SSDs (solid-state drives) in 2.5" and M.2 formats. Each will be in a range of capacities - some of the smaller SSDs might be 120GB, while 3.5" HDDs go up to 8TB now (that's 8000GB).

At this point, a tech-savvy customer will know what he wants and will immediately choose something, or ask pertinent questions of his own. He'll appreciate your efficiency.

But a less assured customer might need help choosing, and that's when you start asking about their budget and intended usage. They probably won't have a specific capacity in mind!

For basic uses like "homework" or "email", you would select a product near the bottom of the price range that fits their computer. For "video editing" you should go straight for the 8TB monsters. For "gaming" you could recommend a combination of an SSD (for performance) and HDD (for large games), using their budget as a guide.

Example conversation:

Cust: I need a hard drive.

Shop: We've got lots of hard drives. What kind do you need?

Cust: What's the biggest one you've got?

Shop: We have an eight-terabyte model. Here it is.

Cust: Perfect! I'll take three.