Frontend, Backend, API on different servers

Hi everyone, I want to build a system with these projects: api.example.com admin.example.com payments.example.com example.com

I'm using AWS as my hosting. Each project needs to be hosted in a different server because I want to use "aws load balancer" for each project. The API will be called from an HAProxy server - http://www.haproxy.org because I'm using multiple domains with SSL but it is not supposed to make any problem.

What is the best why to handle it?

1. Do I need to make one project and split the routes.php file to routes-admin.php, routes-api.php, routes-payments.php in order to avoid duplication of modeling?
2. Do I need to split the projects, install laravel in any server and to duplicate models if needed?
3. Do I need to keep all models in the API project and all the rest project will "call" the api in order to get/edit/delete? of course I will need to use authentication before the "edit/delete" calls...

What is recommended? Thank you very much in advanced!