There is no such thing as "standard English". There is no equivalent of the Dutch "Groeneboekje" in English. If someone is here to learn Dutch, then don't try to "correct" their English with your own interpretation of "standard English"
No it isn't. I speak English natively and "Have you dogs" is perfectly acceptable English. I could just as easily say "Have you a pen?" or "Have you time to go over this document?". All of these are examples of correct English, so "Have you dogs?" should be accepted.
Because that's not really a question in the same sense. You would say that if you were surprised the person had dogs and wanted to confirm. Do you have dogs is the most common form of that question in English.