Using the built-in exporter with individual clips export doesn't give you processed audio or different layers rendered together. It just renders the source clips trimmed the way you put them in your timeline.
I had this problem and ended up making MediaChopper. It is a small utility program that lets you split the video files based on almost any data.
First, you render the whole video file as usual. Then you export the Edit Index from DaVinci Resolve.
Take these two things, put them in MediaChopper and select which segments you want.
Full disclosure: I made MediaChopper and would love to hear if it's useful for anyone.