1. no, it's a cryptographic key stored on your device. but also yes, because if you're using a passkey on a device you sign into using your google account, google can lock you out of that account and potentially that device. if that device is your only way of logging into a service, you'd be locked out of the service in the same way that losing or destroying the device would lock you out of the service. but authorizing multiple passkeys and adding backup authentication methods is encouraged, so for practical purposes the answer is no.
2. you should understand that passkeys are issued by your device or browser. so if you don't want to trust google, you can use a passkey issued by safari or iPhone instead of Chrome or Android. if you're using an apple-issued passkey to sign into some other service that isn't your google account, google has literally no involvement anywhere in that chain.
3. not according to the spec. the passkey is a certificate that gets stored on your device. your device shares a signature (not the certificate) with the service you're signing into to prove you have access to the certificate. but they're issuing you the cert through their proprietary software. if you don't trust google to not snag a copy of the passkey when they generate it for you, you should use passkeys generated by an issuer that you do trust. (in apple's implementations, passkeys are synced through iCloud, so the answer there is yes - apple does have your passkeys and could sign in to services as you if they wanted. google is not doing that.)
4. you'd have to read the ToS for yourself to figure out what you could sue google for. but the more relevant thing than legal recourse is that this scheme doesn't really give google any power they don't already have, and in many ways distributes power out to third-parties so you have to trust google less. apple's passkey implementation is leading google's. others will follow. this is about allowing you to use an open standard to authenticate with your google account.