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I didn't even know there was such a rule. Damn, my English sucks. Хотя даже МГИМО финишт...

It means "If you do go out shopping, then buy me some vodka. But you are not obligated to go out shopping just for that purpose."

Yes, as MA pointed out, there is a small difference in meaning, but it's nothing to lose sleep about. :) In the first one, it is not clear if opening windows will actually help the person to sleep,...

No difference. Just the joy of English. It is a very wordy language. :)