Ok.. as I understand, I can use my original-seed (created during the installation of my former wallet-app)
in order to be able to restore the fund's into Electrum on Tails (without persistence).
Yes.
You need your private keys to access your BTC. And these private keys are derived from your seed, which you have a backup from with your mnemonic code.
Does that mean, all my bitcoin-funds are save(and restorable with the former/inital seed) even the
ongoing transaction is interrupted, e.g. because Tails/Electrum crashes (e.g because of a power outage)?
Yes.
Are "Transaction-labels" a list of the performed transactions?
No. They are not related to the bitcoin network at all.
These are just electrum-specific "names" you can give to transactions. They are only stored on your client-side and are not necessary at all.