What are the REQUIREMENTS for an E-commerce site?

1. Can it be done on a Hostgator shared account? If not, what type of hosting is required?
Yep it can. Good cheap way to start out.

2. Is an SSL required? If so, how much is an SSL and where do you buy one? I use Hostgator, as mentioned above.
If you use a third party provider like PayPal or similar they already have SSL encryption.

3. Can it be built with a Genesis / StudioPress theme? Or am I better off using an actual Woothemes Woocommerce theme? Or something else??
If you're using WooCommerce then ideally you want to be using a theme that is made for it. It's possible to use another theme but you will probably face all types of problems.

4. How difficult will this be for someone that's never worked on an e-commerce site before? (I've got other Wordpress sites but none are e-commerce)
If you know Wordpress then you know how to use WooCommerce. It's just a matter of learning the functionality and were to go to change settings which can be Googled, asked on WF or by trial and error.

5. What other requirements are involved that I might not be aware of?
How will you accept credit card payments? WooCommerce comes with PayPal functionality but if you accept credit card through a different third party then you will need to buy an extension. Other than that its just a matter of configuring all the theme options/woocommerce settings.

Here i would like to answer you all questions.

1. Can it be done on a Hostgator shared account? If not, what type of hosting is required?
Answer:

If you are trying to build e-commerce based website, then best choice is go through dedicate server which help you in term of security as in shared account security or privacy beaches will be there. Go through dedicate package in term of Web Hosting.

2. Is an SSL required? If so, how much is an SSL and where do you buy one? I use Hostgator, as mentioned above.

Answer:
Yes! If you are accepting sensitive information such as pay pal, bankwire details, credit card, etc from your customers through your website must have SSL Certificate security. If you are looking to buy it for as low as price, then go through Platinum Certificate Authorities such as RapidSSLonline.com, and CheapestSSLs.com

3. Can it be built with a Genesis / StudioPress theme? Or am I better off using an actual Woothemes Woocommerce theme? Or something else??

Answer:
If you're using WooCommerce then ideally you want to be using a theme that is made for it. It's possible to use another theme but you will probably face all types of problems.

4. How difficult will this be for someone that's never worked on an e-commerce site before? (I've got other Wordpress sites but none are e-commerce)

Answer:
If you are comfortable with WordPress, then go through WooCommerce as mentioned by pavv

5. What other requirements are involved that I might not be aware of?

Answer:
In else details for eCommerce website, that you need pay pal integration, and credit card integration which you can make it available with plugins.

Guys, I appreciate the help very much BUT I'm thinking about giving Shopify a spin. I'll do their free trial and see what it's all about.

I have four on shared hosting Hostgator account. Just a regular account that allows "unlimited" bandwidth and domains

I don't need one because I am using the authorize.net (DPM) extension and secure payment is taken care of via authorize.net

Don't know about studiopress or genesis, but any woo commerce and probably most woo themes and some people are using Theme Forest themes with the Woo Commerce plugin.

Woo Commerce makes it pretty simple. I love it.

None that I can think of but if you have another question, ask away.

The whole checkout process should be SSL . Also if you have a back-end (admin) side, it should also be in SSL.