Can a buyer and seller use the same agent, yes. Should they, absolutely not.
The majority of agents love being able to work both sides of a single transaction, this way they can forget about any responsibility to either the Seller or the buyer and focus exclusively on earning all the commission. While it's not illegal it should be.
I've attached a link below on how to find a great Realtor, and you'll find a lot more information about this very subject within it that I hope you find useful.