Search for the following:
- Google Auth: Look for Laravel Socialite, a first party package to integrate third-party authentication.
- Cart: Look at this package or similar ones: https://jackiedo.github.io/Laravel-Cart/#/
- API Rest: This might help as to how to build a REST API: https://blog.treblle.com/how-to-create-rest-api-using-laravel/
3 days might be very little time to accomplish all this but everything is possible, wish you luck.
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