After receiving this request, I've now added audio and video tags, that you can use to embed such files from other places. (I've been told Discord allows for easy embedding this way. Just paste it in a message in discord and send it. Afterwards, right click the video or audio file and select "Copy link").
It's using default HTML5 audio and video tags.
There is no straight answer for that question, as support differs depending on browsers and operating systems.
The short answer is:
MP3 for audio
MP4 for video
For the long answer, you can check here for video and here for audio formats that are supported. However, I recommend sticking with MP3 and MP4 formats.