Gm! Thanks for reaching out before I answer your questions, I believe clearing up the terminology for batch mint may help. A batch mint is simply a group of tokens minted together to save on gas costs it isn’t a ‘collection’ or a ‘folder’ An example: Multiple batches minted on the same contract will show up in the same collection on Opensea.
No. A batch isn’t used to organize tokens
No. Batches are no different from minting individual tokens .
If it has already been minted to the mainnet this is not possible but if it hasn’t this is possible.