Multi-Signature – Traditional single signature + multiple signatures using passphrase

Do I need a password to use my existing wallet within multisig (e.g. to send)?

No, unless you choose to sign with Trezor’s key. Considering that you have two master private keys out of three in total, you don’t need access to your Trezor keys, so you don’t need to enter a password. However, to spend using Trezor’s signature, you will need a password because the master private key with the password is not stored on the device.

Quoting wiki.trezor.io/Passphrase:

Passwords are not stored anywhere on your device. Each time you enter it, it will only be used temporarily.

If I don’t need a password but already have funds in my existing wallet, how do I move the funds from my existing wallet to these 3 wallets that don’t require a password and generate multi-signatures?

I’m not sure what you mean here. If you want to move funds from 2/3 Multi-Signature (with passphrase) to 2/3 Multi-Signature (without passphrase), you don’t need access to Trezor. Said above.