Final fantasy 8 riddles

curing status effects?

Not curing status effects or anything to do with the train mission.

Mistakes of the past
are quickly neutralised
The solution amassed
from one red oversized

Hmm, could it be a red Guardian Force, which lets you do things, of which it'd have been a mistake not to do it earlier?

All I can think of here is Phoenix and Ifrit.

My guess is the following:

Mistakes of the past are letting party members die.
They are quickly neutralized by a Phoenix Down/Pinion.
The solution is amassed,
from one red oversized, yeah, Phoenix has a lot of'em.

It's not a GF, but the red oversized is something living.

Living organically or mechanically?

Organically.

It wouldn't be the Moomba would it, when you use the Friendship Item from Chocobo World, which lets you summon it in battle?

Nope! I might also say that the red oversized isn't the answer you're looking for, but rather the "solution".

Hmm, is the auditions for the musical sequence, where you can try out different instruments on the characters but only two combinations sound good.

Hmmm, is it Norg?

In the battle you have to keep hitting the pods to keep them blue-

Mistakes of the past - not hitting the pods to keep them blue
are quickly neutralised - by attacking them
The solution amassed
from one red oversized -the big red pod

he is organic (inside) and it is done via menus (battle system)

is it the GF, Carbuncle?

None right so far, but nice thinking with NORG. The menus I referred to in my earlier hint aren't battle menus though, but rather one of the menus you can access via the triangle button outside battles.

Uhm,

Using a Phoenix Down to revive a dead player.

Mistakes of the past - letting them die
Are quickly neutralised - quick to do
The solution amassed
from one red oversized - Phoenix Downs are in fact large down feathers from a Phoenix

Is it the seeD exams that you can take from the menu, as with missions you can decrease your rank if you perform badly?

Neither. Remember that the "mistakes" are only mistakes if you consider them as such! Letting a party member die is definitely a mistake except in very specific circumstances, and I don't think your SeeD rank dropping is ever anything else than a mistake.