It's possible, but you will sound very "quaint". This is the old grammar form. My suggestion is to follow the "do you have..." pattern as your standard phrase. "Have you got..." is very common, but is more a spoken form than a written one.

Basically no. "Have" does not function in this case without either "do" or "got" - I do not know the grammar rule as to why, but they are not optional as opposed to the Russian "есть" in the phrase "У меня есть...". Is there a form such as "Have you a car?" that is acceptable (such as in Great Britain)? I cannot recall ever hearing this, even in British English. Suffice it to say that if you speak that way to most English-speaking people it won't be accepted. There is a GREAT discussion of this type of question at http://separatedbyacommonlanguage.blogspot.com/2011/05/do-you-havehave-youhave-you-got.html. It remarks there that questions require either an auxiliary verb or "do" at the beginning, "have" being an auxiliary verb.