I tried "Is the school on your street." There may be a reason that is incorrect, but I do not know what it is.
Why is твоей used here and not твой? I didn't quite get the difference yet...
Твоей is the prepositional singular feminine version of твой. So if твоя улица is the object of a preposition like на, it becomes твоей улице.
No, that would be «У ва́шей у́лицы е́сть шко́ла?». However, even that is likely to be understood "Is there a school near your street?", because streets usually don't own schools.
Whithout есть this sentence would mean either "Is the school on your street [or on the other street]?" or "Is it a school on your street [or is it something else]?" depending on the emphasis. By adding есть we clarify that the question is about the existence of the school.