"Do-support" doesn't come from the Normans (not technically the Franks) but most likely from Celtic or Welsh language influence in Britain. But yes, this came later in Middle English and verb-subject inversion for questions was indeed the original syntax in English and other germanic languages.
And we still see it in constructions like "are you cold?"
I couldn't differentciate between Er and Ihr, and you've no idea how many times I've failed because of this. So I googled how to tell the subtle differences apart, and it said that Ihr is Ear, and Er is Air.
So I was like "YES! I will FINALLY get it right!"
Hat Ihr Hunde
Nope, it was Er.
Seriously, they need to redo the audio recordings for those words.
Your question is extremely vague. Without further explanation, "this" has to mean the entire sentence, and sentences aren't in cases like that.
"Er" is nominativ, and "Hunde" is akkusativ. That is, "Er" is the subject and "Hunde" is the direct object. "Does he have the dog?" would be "Hat er den Hund?"
Given that this is a question, Does he have dogs? is the best way to put it. English often uses more helper words (does in this case) than other languages, especially when you're asking a question.
Has he dogs? would be understood but is a very odd way to phrase it - note that this is an exact, word-for-word translation of the German, but in English it would seem very old-fashioned to most native speakers.
Has he got dogs? would also work - again, more helper words than most other languages.