Will the passphrase be required to use the existing wallet inside multisig (for sending, for example)?
If you didn’t choose to sign with the Trezor key, don’t. Since you have 2 private master keys out of a total of 3, you don’t have to access the Trezor key, thus, no need to type the passphrase. However, if you want to spend with a signature from Trezor, you will need the passphrase, because the master private keys containing the passphrase are not stored in the device.
The passphrase is not stored anywhere on the device. It is only used temporarily when you enter it.
If I don’t want the passphrase required, but I already have funds in the current wallet, how can I start transferring funds and creating multisig with these 3 wallets, as no passphrase is required for that existing wallet?
I’m not sure I understand what you mean here. If you want to move money from 2-of-3 multi-sig (with passphrase) to 2-of-3 multi-sig (without passphrase), you don’t need to access Trezor, as I do said above.