A.C.
I don't know I would trust anything like that on FB. But, if you're confident it's ok then.......
Yes. You would certainly have to pay taxes on the $1,000. I have been lucky enough to win exactly $1,000 in the past and I had to pay about 30% taxes on it. They will not take that out before giving you the check though. When you cash the check you will have to buckle down & save about $300 of it for tax time. You will receive a tax form for it next year so you can claim it as income.
No idea on how the commercial thing would work. I can only assume they would pay to come to you or pay for you to come to them to film but I'm sure the details would have to be in the fine print.
Good luck!