If i am trying to sign up for a site such as Hydra Networks, (affiliate application)
I would be an "individual/sole proprietor"
If my web site was 100% mine.
Correct?
That would be correct, unless you want to go through the hassle of getting an EIN, with an eye towards forming a much larger business with employees later.
That is correct as well, although you can deduct business expenses and other expenses related to running your business. You'd have to see a tax professional for all the ins and outs on that. The affiliate in questions will report any income paid to you to the IRS, and so you must report it on your return.
