Omar, (AmerEng) technically that is a correct sentence, but a lot of things need to be established beforehand. For example, it tell you that I am going shopping before I go to your place. You call me to ask me to buy something, and ask "are you shopping?" To sound better, I suggest adding a word like: "shopping, yet", "still shopping", "shopping already"

Yes

It is gramatically correct, but it depends on the context, Omar. Some examples: I'm on the phone with a friend and I hear supermarket noises in the background. I see my housemate looking at Amazon.com