Indeed, all you need to do is route the outputs of your soundcard to the mixers input together with the outputs of your hardware and dj-setup. For recording into the computer simply use the master output or busses and route those back into the inputs of your soundcard.
It's also handy to use the controlroom output for your monitors, in this way you can control their volume without affecting any other signals when recording.
Your outboard gear can be used via inserts or aux.