In clear words, where are the transactions that happens between opening and closing channels stored and how immutable is it?
The transactions are stored by both parties involved in the channel. Lightning software does this automatically.
They are just as immutable as any other bitcoin transaction. Lightning channels are a 2-of-2 multi-sig, so both parties must sign every transaction, and neither party can edit or modify the transaction without invalidating it completely. The risk is not in one party being able to change one of the transactions - as I said, this is impossible. The risk is with one party attempting to broadcast an old outdated transaction which favors them more than the most recent transaction. But as I mentioned above, if one party tried to do this, the other party can take all their coins as punishment.