The general rule is that the poor of your own city come before the poor of elsewhere. Thus, if you have poor people locally, you should give to them before giving to people in Eretz Yisroel.*
As for whether or not a particular beggar is Jewish, I will say this: We strive to emulate HKBH. By Him it says “Tov Hashem lakov v’rachamav al kol ma’asav.”
The Wolf
* That is, of course, assuming you don’t live in Eretz Yisroel.