Acid Water Neutralizer - How To: AquaPure Neutralizer use and maintenance
"Clear water iron" would be a search term to help you understand that side of the problem. While it can be treated, an acid neutralizer is not going to treat it - it needs to be oxidized (aeration/spray or chlorine are typical approaches) and then filtered out.

An acid neutralizer (generally, no idea on your specific model) does pretty much what it says, often by using a bed of limestone chips (low tech and simple) or possibly a more soluble alkaline chemical. The probably closely related "APUN100-LM" manual does say "Media, calcium carbonate" which is fancy language for limestone; you'll just need an appropriate size (too coarse, not enough surface area - too fine, doesn't stay in the filter housing.) Actually, I think that -LM nomenclature simply means "less media" (it's shipped without any, you source it locally) so that probably IS your manual.

Since the green stains in the plumbing  are from your copper pipes corroding, it's probably a good idea to get that working again or functionally replaced - especially if your copper plumbing is old enough to have been assembled with tin/lead solder. Acid water dissolves copper and lead, which both poisons you and will eventually perforate your pipes.