Hello djAnton,
let's clear a bit the confusion.
Previously I used the myNext wallet and moving to the Nxt Client. I'm a newbie and not get it fully. I've managed to download the passphrase file. And also to decrypt it. So now I've several things to fill in somewhere. But I'm a bit lost.
I've my password to get into myNext wallet (is useless now, I guess)
Correct, once you have downloaded & decrypted your myNXT wallet and you can access the Nxt account using the Nxt Client, you don't need the myNXT master password anymore.
I started the Nxt Client. It asked whether I'm new or returning. I choose returning and it asked my account address: NXT-etc-etc-etc-etc. Then I started downloading the Blockchain (it still is....). I saw my balance (public information?) and later it disappears in my dashboard (now it's 0, all of a sudden
)
When you open in the Nxt Client a specific NXT address, as you say there's only public information visible. You're seeing the account with the official Nxt Client interface, but other than that it's not essentially different from a blockchain explorer. In this sense, you haven't really "logged in" to the account. To send any transactions, or to access any private data (like contents of an encrypted message received in the account) that's when you need to prove you own the private key for the account - the passphrase you obtained.
And the balance is 0 because, as you chose to install Nxt as full client and not light client, it is downloading to your computer a copy of the blockchain. And then your Nxt Client only knows about the blockchain blocks that have been retrieved so far. This means that you'll see the account balance corresponding to the latest block you've downloaded. Once the blockchain is fully downloaded, you'll see the account balance and details updated to the current Nxt block.
I haven't fill in any passphrase yet. I see a 'set account info', there is a field for a password. Is that yet another password or should i fill in the password (long String) that is encrypted in the downloaded file or do I have to fill in the 'restore passphase'?
I think I answered this above, but as said, the passphrase is only needed when you have to prove ownership of the account. This is decrypting any encrypted stuff for your eyes only, or signing/sending transactions from the account. Other than using it when the client asks you to introduce it, remember to keep the passphrase securely and privately saved because it is the real key to the control of your account.