The confusing "ein"
What is the point of adding "ein" to the end of this sentence ? (Sie kaufen in einem Supermarkt "ein".)
I'm No expert, but if i saw the first one, and i had to choose, i'd translate it as: they shop in a supermarket. the second one, I'd think of it as: they buy in a supermarket... But that sounds odd, so I'd probably choose "shop" for that one too. Probably best to wait for a native speaker :)
Native speaker here. I agree with all npLam said.
It's very similar to English (to shop vs. to buy). "Sie kaufen in einem Supermarkt" sounds unnatural. And if you buy something at the supermarket, you'll usually say, "Sie kaufen Äpfel in einem Supermarkt", but "einkaufen" more or less works, too ("They shop apples at a supermarket").
I agree with stepintime. For me, as a native, "Ich kaufe im Supermarkt "is a bit unnatural and has a feeling of "I (generally) buy (stuff) in a supermarket." while "ich kaufe im Supermarkt ein" is that I am actually doing it now.
The verb, as in your other example, is "einkaufen" and is separated between "ein" and "kaufen" - ich kaufe ein, du kaufst ein, er/sie/es kauft ein, wir kaufen ein, ihr kauft ein, sie kaufen ein.