[Help] Recording Podcast on XENYX Q802USB to Adobe Audition?

From your second picture that shows USB Audio Codec for the record and play devices, it looks like Audition is seeing your mixer--many/most Behringer devices show up as USB Audio Codec.

A couple of suggestions:  first, for recording, set up a new Multitrack session, making sure the settings for Sample Rate and Bit Depth are the same as the mixer (probably 16 bit/44.1kHz).  Then, on the track you want to record to, go to the input selection (in the control panel at the left end of the track, a drop down menu marked with a right-facing arrow)   Click on the box (which will likely say "None" to start with).  You'll get a box offering something like "None (Default Stereo Input), Mono, or Stereo.  Click on Mono it it should offer you the option of USB Audio Codec 1 or 2....select 1.  On your mixer, pan the mic channel hard left.   If you ever want to record 2 mics at once, make another track's input USB Audio Codec 2 and pan that channel hard right on the mixer.

Playback will be via the mixer as well.  On the box marked "USB/2-track" select the "To Phones/Cntrl Room" option and this should give you sound either to monitor speakers or headphones plugged into the appropriate socket.

One thing to note is that, due to limitations of your mixer, you'll have to monitor your mic after a round trip via your computer.  This can result in annoying latency.  Minimise this by setting the latency/buffer size on Audition's Audio Hardware menu as low as you can get away with before you start to get glitches in your recording.