Hello again gregory,
Yes, then you are classified as an independent contractor. The money you make from this company has no tax withheld, and at the end of the year, they should send you a 1099 Form to report your total earnings for the year, although if your earnings are less than $600 for one year, then they are not required to report them.
You will report this income on Schedule C as a self employed person, even if you have additional income from a regular job. On Schedule C you would report the earnings from this company, and you would also deduct any expenses you had in connection with this business. Those deductions could most certainly include a deduction for the business use of a portion of your home, as long as that part of your home was strictly used in relation to your business. For most people this usually means having one room that you have dedicated for your office use. (You could not have a computer in a room that you also used for your bedroom and classify that as business space).
As an independent contractor you can deduct other expenses related to this business, such as depreciation on your computer, office supplies, software you purchased in connection with maintaining your website, cost you paid for website design, etc.
After deducting your expenses, you will then be liable for federal and state income taxes on the net income, and also employment taxes (social security and medicare).
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Thanks and let me know if you have more questions.