hola, oldgringo... Your sentence is wrong because you need to say... In my country THERE are conflicts. Hay = there are. One could also use "existir" in the Spanish sentence... En mi país existen conflictos." Then in English you could say... In my country exist conflicts. In other words HAY = EXISTIR. Hope to have been of help =)
The indicative third person plural of haber is "han" if I'm reading my dictionary correctly, so why is the Spanish translation of "there are" "hay" here and not "han"? All I can think of is that conflicts is not the subject here but rather there is an "assumed" singular subject in a "there is/are" sentence. Thanks.