“Are you saying that the Yiddish and Hebrew word mean the same thing but are spelled differently?”
without question.
This comes up a lot with last names where the origin is yiddish. For example the name Goldberger. In Yiddish it is quite lengthy גאלדבערגער with the א…ע..ע serving as vowels, however in Hebrew the vowels are nekudos though often omitted/assumed thus an Israeli might spell his name גלדברגר. Its the same name, pronounced the same one is spelled in yiddish the other in Hebrew.
Thus the word נער pronounced Nar is not a yiddish word. There is a yiddish word that means the same thing and is pronounced the same way, and stems from that word. To get the word pronunced Nar in Yiddish it is spelled נאר.
OTher than names I cant think of any other such example at the moment, though Im sure they are out there.
As for your last question the correct spelling is בײנאכט. different locales pronounce that differently as Baynacht Bynacht so the spelling may have shifted to באנאכט. You have to keep in mind most Yiddish speakers dont really care what YIVO has to say. so there isnt really a formal body governing the “correct” spelling of words. Im sure you will find the word fool spelled נער in some places though it isnt technically the correct yidish spelling. Furthermore there is generally no formal yiddish grammar class that most current speakers study. I did have a basic spelling book/class in the second grade but after that we just learnt by rote and “what sounded right” based on what you heard