Alcohol makes your blood vessels dilate (they get wider so the area through which blood can travel is larger). This answers 2 of the parts of your question. It means that the blood vessels take up more space, so blood vessels close to the skin get even closer to the skin, giving off some heat to the local area and maybe giving you rosie cheeks.
Blood vessels dilating means that there is less pressure within each blood vessel to keep the blood flowing. So your blood pressure decreases. In order to compensate, your heart has to beat harder and faster to return your blood pressure to normal.
Interestingly though if you continue to drink more alcohol, it will actually cause your blood vessels to constrict again.
Not sure about making you out of breath though.
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