xDAI is an Ethereum sidechain that operates a POS (Proof-of-Stake) validation mechanism (the new validation mechanism used in Ethereum 2.0). xDAI uses the same wallet system and signatures, meaning that your Ethereum wallet will work with xDAI.
On DMEX xDAI is only used for trade processing. All funds are stored on Ethereum as before.
No. You do not need to do anything, xDAI is integrated as part of the stack and is not affecting the user in any way. You simply deposit to DMEX as before on Ethereum network.
Ethereum contracts are connected to the xDAI contracts through a decentralized bridge that relays messages between the two chains.