Which machines can I use to fight with in the Underground Colosseum

Aside from analyzing the BGM and looking cool, the HUD Sound Waves chip serves one other purpose. According to posts like the one in this thread, it helps you find a specific Pod in the desert:

There's an item in the desert (pod C) that emits a high-pitched sound when you're close to it so it's easier to find. The sound display detects this noise, giving a hint to people who can't hear it (or hear poorly in general, or people like me who thought my speakers were dying instead of thinking it was an actual game sound).

This is backed up in this thread, as well:

I believe it's meant to help those who have a handicap with their hearing.

There is an thing (a pod) in the desert that can be found through a sound it makes. Not everyone can hear it.

If you've already found this Pod or are confident in your hearing abilities, there appears to be no other purpose to this chip other than being a BGM analyzer.

Ok, I played through again starting from scratch. The chip that shows chests (and harvest points) on the map can be had near the end of the B route play through. Immediately after I acquired it, I could see only one chest on the map. I had completed Sorting Troubles 1 already. One chest remained marked until Sorting Troubles 2 became available near the beginning of the C route play through, and then two chests appeared.

I completed that quests, and the chests were removed from the minimap. Leaving the camp though resets them so they show again, but because the quest is complete you cannot access that area again. The chests don't contain items; they are key items required to complete the two Sorting Trouble quests and seem to return when leaving the area.