First, I would like to mention that upgrading to Trezor Safe 3 is a good idea! Please, find answers to your questions below:
Yes, you can simply recover your 24-word recovery seed from Trezor Model One or you can create a new seed (12-word) and move the funds from your Trezor Model One to your new Trezor Safe 3 by sending them via standard transactions.
Information on how to perform the recovery process for Trezor Safe 3 can be found at https://trezor.io/learn/a/recover-wallet-on-trezor-safe-3
No need to worry, there is no problem with it.
There is nothing like advanced recovery with Trezor Safe 3 as even when doing a standard recovery with this device, you need to enter the seed directly to the Trezor device. This is actually a great benefit of Trezor Safe 3