I already have bitcoins in a paper-wallet (and a bitcoin-core ballanced zero). Can I send those bitcoin directly from the paper-wallet to a new Trezor?
Yes, import it into Bitcoin Core.
If not, how do I import the paper's private-key to core (0.13.1) first? Does it require miners' (transaction) fees?
How do I create secure seed-words?
Use the steps above, given by LoyceV. This step does not require transaction fees. Transaction fees is required when you send the coins to your trezor wallet.
There should be a guide for Trezor in the package that came with it.