Installing unauthorized apps.
No, Google does not install unauthorized apps.
secure Linux-based OS.
Android isn't exactly a GNU/Linux based OS if that's what you mean. Android uses the Linux kernel, but has a totally different OS core from what you normally see in so called linux 'distros'
How to completely remove Google from an Android device?
The best alternative remains flashing an AOSP based custom ROM that doesnt bundle with GSF (Google Services Framework) and Google Play services.
The next best thing you can do right now is using ADB. Download it from here
⚠ You haven't mentioned your phone's OEM, OS, Version, etc so I can't exactly know how your device might behave once the below command(s) are executed, things might break.
The command to uninstall an app would be (even if that's a system app)
adb shell pm uninstall -k --user <user id> <Package name>
For example to remove Google app for user 0, it would be
adb shell pm uninstall -k --user 0 com.google.android.googlequicksearchbox
Incase your fork of Android restricts Google app from being removed using ADB, i.e., if an error pops up upon executing that command, try disabling it via ADB
adb shell pm disable-user com.google.android.googlequicksearchbox
Similarly, for Google Play services and Google play store, the package names should be
Google Services Framework is