Open Solmi's MP4 to MP3 converter in any browser, drop the video in, choose an MP3 quality, and press Convert. The browser decodes the file's audio track on your device and re-encodes it as MP3, so nothing is uploaded and there is no size cap beyond your device's memory.
Two ways. Open the converter in Safari and use it exactly as on a desktop. Or build a two-step Shortcut: Select Photos, then Encode Media with the Audio Only option turned on, then Save File. iMovie and the Photos app cannot export audio on their own.
Open the converter in Chrome and drop the video in; it runs on the phone, not on a server. If you prefer an app, any video editor with an 'export audio' or 'extract audio' option works, but the browser route needs no install.
Slightly, in theory. The audio inside most videos is already compressed (AAC), and MP3 compresses again, so pick 192 kbps or higher; at 320 kbps the difference is inaudible on normal speakers. If you need a lossless copy, use ffmpeg with -c:a copy to extract the original AAC track without re-encoding.
On iPhone, open the video in Photos, tap Edit, and tap the yellow speaker icon to mute it. On desktop, ffmpeg -i input.mp4 -c:v copy -an output.mp4 strips the audio track without re-encoding the picture. Most phone video editors have a mute or 'detach audio' control.
MP4, M4V, MOV, and WebM in the browser tool, since those are the containers browsers can decode. For MKV, AVI, or anything exotic, use VLC or ffmpeg on a desktop.