Hi, for this to happen you need to use API (best way) and external calls to those endpoints, or you need to load a laravel application instance in your homepage to get what you need (uses more server resources and less practical), also you can define an external connection and pull data out from the db directly (worst way, you will lose lots of stuff).
For some basic examples and pre-built API solutions you can check DisposableBasic addon, it provides some endpoints for VA admins to pull data out of v7.
LiveMap is a different subject, it runs with java/rivet calls, so it is already possible to implement it somewhere outside phpvms v7, check how the map widget works and mimic something outside.
Good luck