I use muvaudio to convert files to other formats. When I was ripping all of my CDs, I forgot to change the format and some ripped to m4a. I switched them over to mp3 at 320. As for losing quality? I have no idea, I didn’t notice any but I’m not particularly fussy about that (and most who are, wouldn’t touch mp3 format anyways).
An MP4 is just a container format. It can contain any number of codecs, MPEG-1 Layer 3 (aka MP3) is just one of them.
You really need to somehow see what codec is being used to know how well it can convert, but it will convert to any lossless format (like FLAC) or a really high quality lossy format (like MP3 360K) without any noticeable loss in quality.
You can convert anything to FLAC without losing quality. However, you cannot convert from one lossy format to another without degradation. Honestly, I wouldn’t bother transcoding, especially not without checking the bitrate of the source file.
M4A is just another suffix for AAC; it’s certainly not a lossless format. AAC is similar to MP3, but it’s a newer format and offers higher sound quality at the same file size. Thus, if you’ve already got a song in M4A format, you can only lose quality by converting to MP3.
Apple reckons that a 256-bit M4A is about the same sound quality as a 320-bit MP3, and I haven’t heard any contradiction of this.
Most modern music players support AAC, so there’s really no good reason not to use it.