When will the Bitshares Exchange be launched?

It is currently under development. Our focus right now is making the server as lightweight and robust as possible. The goal is to future proof our build because BTS nodes requires such an incredible amount of resources. Also, we want to a be as decentralized as possible so we're looking into which coins we can implement into the gateway portion while staying true to that ethos. Right now Ethereum smart contract wallets seem to fill that niche best. Which would serve as a bridge for Ethereum and ERC into the Bitshares network.
So by the end of the year we will have the Bitshares exchange launched.