What settings can I use to export a video as an MP4 but keep the audio the same as the source?
To a certain extent, this will depend on the audio encoding of the original source, which you haven't provided.
Otherwise, Mp4 video uses AAC audio which is *lossy*, meaning AAC - by the nature of how it works - will degrade your original audio a little bit.
You can edit the export preset to make certain the export bitrate is 256KHz, but that's really all you can do.
Also, Hitfilm is using the OS encoders, so your ultimate audio quality is based on how good the Microsoft encoder is. FXhome has no control over that.