No, you shouldn't import your wallet because that includes entering your Trezor seed into a web wallet. The seed and everything it holds would then be much less secure, and you essentially turn it into a seed from an online web wallet. Don't do that. Creating a new wallet and connecting the Trezor with Metamask is what you want to do. In that case, your private keys remain on the Trezor and you will be using Metamask as the software interface instead of Trezor Suite.

I use the Bitcoin-only firmware with my Trezor, so I can only speculate why that is. Perhaps you need to add every single token in the settings of your Trezor Suite. Or it could be that Trezor Suite doesn't support those particular assets. Take a look at https://trezor.io/coins and see if your tokens are supported there in Trezor Suite. If they aren't, you will not be able to see them. But that's why you have Metamask, to interact with your tokens through that software. Also, you can always check everything you need to know about your address on Etherscan.

Both? What's the second one? OP's coins/tokens are on the Trezor, not on Metamask. Metamask only has his public keys if he established a connection to it with his Trezor. No transaction from the hardware wallet can take place without a physical confirmation on the Trezor.