Google has the capability to read everything that you can read on an Android phone, unless you have taken steps to remove all Google-controlled components that have system-level privileges. Last time I checked, this included Google Play Services, which are installed by default on most Android phones.
Note that messengers with end-to-end encryption, like Signal, cannot protect against an adversary with full access to your device.
This is part of why people de-Google their phones, which usually means replacing the entire OS with something like LineageOS or GrapheneOS.
Of course not. End-to-end encrypted messaging protects against eavesdroppers in transit. It's an opaque envelope.
(Edit: Keep in mind that Google is not the only potential eavesdropper out there.)
What it cannot do is protect a message from someone reading over your shoulder when you write a message or open an envelope. On mainstream Android, that could be Google, if they choose to abuse their system-level access. On iOS, it could be Apple. And so on.
Those companies might be eavesdropping on sent/received messages already, either at a large scale or in a minority of cases, or regionally, or they might not be doing it at all... yet. But they have the capability. You'll have to decide for yourself whether that risk is acceptable.