I've done this with pro software, but you can get Shotcut for free - your MP4 will consist of the frames and the audio profile in separate tracks. Once that's loaded, you can drop in the MP3 as an alternative audio track, either adding to or replacing the MP4's audio (up to you and you can easily mute tracks to see how either sounds).
As already mentioned, there are usually tools that will help you move or stretch the audio to better fit the timeline (you can't stretch it too much or it'll start sounding really weird).
When it comes to being looped, you just need a player that can do that - VLC has a repeat function.
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Alternatively, you can probably make a Powerpoint presentation that will do this - these days it has some pretty powerful tools for multimedia.