Bitgree is a non-custodial service. Wallet is generated in the user's web browser, and Bitgree does not have the private keys from user's wallet. Escrows are also non-custodial, as 2-3 multisignature contracts (signers are wish's user, proposal's user and Bitgree).
For usability reasons, an encrypted copy of the user's wallet is sent to Bitgree. But the encryption password is never sent, so Bitgree cannot access the user's private keys. Wallet decryption process always is done in the user's web browser.
Yes, you only need to use the seed words of your Bitgree wallet, which you will find in the Advanced Wallet section. You will also find there the derivation path you will need to use.
It's not possible. The user's wallet is never sent decrypted to the server; the user's original password is required to decrypt it. And the user's original password is not sent to the server either, only a hash of it is sent. Therefore, if you lose your Bitgree password, you will also lose access to your wallet.
To avoid this, we recommend that you make a backup copy of the seed words of your wallet. That way you could always access it in an external wallet, like Electron Cash.