I don't know how they handle cash deposits exactly, but bitsquare has arbiters who resolve disputes. When you send BTC on there you send it to a 2-of-3 multisig where both parties to the trade can agree to release the BTC to the buyer (in case of no dispute) but if they don't then the arbiter decides.
You have to use your regular Monero wallet. Bitsquare's client only handles the BTC, not the other coins/fiat. Use the standard monero CLI (or GUI eventually). Do not use MyMonero or an exchange. You must be able to retrieve the tx-key to prove payment in case of dispute.
Oh ok, so who gets to be an arbiter? Does it base off of someone who created the software to pick people, or is there a trust rating system on there or something?
And that makes sense about using your own Monero wallet, but what prevents you from using the GUI? I use CLI but I'm just curious as to why.
Also, what method (if you have done more than a couple trades on there) would you suggest on using in terms of paying/receiving USD?