Literally the translation would be: I have been studying for a month = He estado estudiando durante un mes. However, in Spanish we could understand that you are done with studying. For example, you have been studying for a month, you took an exam and end. If you want to say that you have been studying Spanish for a month and you continue studying it, your translation is perfect: "hace un mes que estudio español".

Yep, and the alternative form is: "llevo un mes estudiando español" (llevar + tiempo) More literal: "he estado estudiando español durante un mes" (pretérito perfecto contínuo) I hope it helps