No, it could not. 'Svůj' always refers to the subject of the sentence. Therefore:
'Do you see your house?' = 'Vidíš svůj dům?'
'Do you see my house?' = 'Vidíš můj dům?'
'Do I see your house?' = 'Vidím tvůj dům?'
'Do I see my house?' = 'Vidím svůj dům?'
It gets slightly complicated in 3rd person (at least on the English side):
'Does he see his (own) house?' = 'Vidí svůj dům?'
'Does he see his (someone else's) house?' = 'Vidí jeho dům?'
Thanks the Gods I found this explanation. I just lost more than an hour trying to understand the svůj vs můj vs tvůj logic. My head was about to explode. Maybe this explanation should be added to the "tips and notes" page. It's just that the sentence, "Svůj very loosely corresponds to the English “own” and indicates the possession by the subject of the clause" didn't make sense to me because, to my knowledge, there is no such word in English (but, especially in French for me) like this "Svůj". Thank you so much E_S :)
No, it does not. The above order is the most common there is. The one you have is slightly unusual and I would only use it in a situation where I am showing somebody something and they are having hard time locating it. So i ask "Svuj dum vidis' as a kind of a confirmation that he/she indeed sees their house and I am now going to use their house as i point in space and tell them to look left or right or up to whatever of it. I am upfront assuming that they do see their house. If I only wanted to know if they see their house without assumption, the above sentence would be ideal. You can tell it is a question from the intonation.