US taxes in DR? Confused

I'm returning to DR to live I hope this time forever.
I have some questions about taxes and such. I have asked my old accountant here in USA he said one thing. I called another and he said something else. I do not understand all formal language when I read the info on line about paying USA taxes when living abroad.
So heres the questions.
I have a web site now. I am making a little money from the affiliates and paid advertisers. How do I claim this when I live in DR? Do I have to claim this? If I have to claim can I use all the typical business deductions, office (home office in DR and physical office rental), fees, mileage, tickets to and from DR since it is a sight about DR, cost of computer and servers and such?
I would rather not do the taxes so if I register the site in DR as a business there then do I have to pay taxes in DR?
Or should I just say forget it and not worry about taxes at all?
I know there is a certain amount of money one can make in another country where they do not have to claim but what about a business or money making hobby?
I have asked the questions to many in USA and I get different answers each time.

So, I would need to file as a business in USA. Claim all my deductions, mileage, office expenses, profit and loss, cost of going to DR. Taxi fees, rental of an apartment and all could be deducted on my USA taxes then? I do not make much income with the site and I have no other income.
How does one go about filing a business tax return for USA while living in DR?

If I plan not to return to USA, run the web site from DR, who would get my taxes? If I need to pay the tax to DR can that be claimed as expenses on my USA tax return? If I never live in USA again do I still need to pay taxes in USA?

One accountant I spoke with did quote that under a certain income that one does not need to claim anything. My only income is from affiliate payouts from my web site and for paying advertisers. What would this income be considered as?
According to the post Anna made I would have to claim taxes in DR. Would the payment of these taxes be claimed in USA as a business deduction (cost of running a business)?
The income this last year is not much. Maybe less than $2500 and after you calculate the expenses, computer, internet, programs and all it is maybe half that much as clear income. But next year there will be more (I pray).
I wouldn't worry normally but the affiliates are registered under my social security number.

So the money I made the beginning of this year while living in usa I do need to file in USA? Even if it is only affiliate income from placing others ads on my web site?
Then once I am in DR. I will be running my site from there. Does this then count as foreign income or is it still USA income? I will be receiving monies from the affiliates plus getting money from Dominican advertising. So the Dominican money would be foreign income and the american money, no matter how small the amount, would have to be filed in USA?

So it would be paying taxes 2 times? In USA and in DR?
This is web site income and not that much. Could it be considered a hobby by any chance?
So I would keep track of every expense. Like the price of extra luggage to carry my computer to DR, my rent, my office space, my tickets, transportation-mileage in DR? Just as I did when I had a real business in USA (this is the first year that I had a web site).
This way my business would never make a profit (so far this year I made almost $2000usd). It will be minus big money!
So then what about the local and state taxes if I do not live in USA?
This is just so confusing to me.