When you film in slow motion mode, the video created will have no sound, but there will be also a audio file.

What can do with this audio file?

Hi Ya Aku, there will be.AAC audio file when you connect the Osmo Action to the PC, since the video duration is lengthened, the audio doesn't match, you can just ignore it.

Can I use this audio file to the video? I accidentally recorded a long event in slo mo, then sped in up in Final Cut 8x. Can I do the same with the audio?

you can add audio in Final Cut .  8 times speed up for video and export the video+audio to get a normal speed video.