My 7 month old randomly gets purple hands and feet a lot. Is this normal?!?!

Pretty normal. Older children and adults control their temperature if they are cold or ill by decreasing circulation to the hands, feet and area around the mouth, reducing heat loss and causing these areas to look bluish. Normal infants and toddlers can have this reaction at random times unrelated to temperature. If a child is blue all over, or has breathing problems or fainting, more evaluation is necessary.
Heat conservation. Babies have some systems that conserve the heat their metabolism creates.Shifting blood flow from the top skin to the deeper skin, often gives a darker appearance to fingers/toes/ears & lips.The same area will blush pink if you put it in warm water. Some have concerns that this means poor oxygen content; a better place to look is the inside surface of the eyelid that shows what the brain gets.
Normal. It is a condition called acrocyanosis-that is , only the hands and feet turned blue/purple. This will resolve on it's own in due time , about 6-7 months old.