@OP If you are in New York state and you file as an Individual, reporting Self Employment earnings on Schedule C, with the I.R.S. on your Federal return you will need to pay Self Employment Tax, if your Net earnings are more than USD$400. Probably, if you have Self Employment earnings above a certain amount, that will be included in your Taxable Income, on your New York State Income Tax return.
Consult a C.P.A. or Enrolled Agent, for accurate information. I am *not* a tax professional.
If Hostgator can handle .cl domains you should be fine with them.
Whether or not you charge your Chilean customers their local tax (VAT or IVA?), if you are not located in Chile, is another matter and I don't know the answer to that one. Possibly you can get that information from the Chilean tax authorities in Santiago de Chile.
Not sure about the cPanel in Spanish question. Suggest you search cpanel.net for that information. GL and welcome to WHT