Are you able to post a screen grab of your Sequence (timeline) so we can see your layout and track management.
It should be no problem at all cutting a simple 2 video conversation with 2 audio tracks.
Audio FX can definitely be applied from Audio Track MIxer.Its a twirl down menu.
Not sure about the clip Mixer but I dont think so. I never use it for anything.
Usual workflow is FX on split tracks via Audio Mixer Panel