Can i also Burn with 1.2.5 or i need the 1.2.5.1?
When i will Burn 10k BLK
then i must:
burn 10000 "Public key"
Then i must update on 1.2.5.2 and i can stake with my old wallet dat BLK "old"?
Yes. Also you can use 1.2.5 with account generated on site:
https://blacknet.ninja/generator.htmlcan i enter new blacknetkeypair command! Will the new mnemonic key be valid for the previous public key, for which I did not initially save the mnemonic key

Creating a new mnemonic will make a new key. it won't be linked to a previous key pair.
If you didn't save the mnemonic for the public key you used when burning blk, I think the blackcoin and the blacknet tokens are both lost to the void forever.
I think we can replace the key, if he proves ownership of burned BLK and there are no objections.