You have to have Bitsquare open in order to use it?

Is my understanding of Bitsquare correct, in that the only way you can use it is to have the bitsquare desktop client open in order to use it? You can not make a listing and shut down and are able to get a message saying that someone has accepted your offer?

If you are the offer maker you need to leave it running because there are no server who host your offer and the key for signing the deposit tx is only in your app.
Though as taker or as soon a trade has started (if someone takes your offer) you don’t need to stay online, but you need to check from time to time about the state of the trade (confirmed fait/altcoin sending/received,…).