I've already integrated API GET and POST to other websites. But i don't know how to receive a POST. Where does it go and how do i handle it?

Access itself doesn't really "listen" for API calls. That's what a web server does: it sits there waiting for requests, then responds to them. Access is a desktop application, so it doesn't have that kind of built-in listener.

That said, you can set up a sort of de facto Access server if you want it to act on outside data. That's what I do in my office. My data lives in SQL Server, but I have an Access database that runs on a loop. It checks things every minute or so, processes requests, sends out email, and pulls in information from my website, etc. It's not technically handling API POSTs, but it's achieving the same end result.

For example, every morning I manually download my PayPal transactions and my YouTube member list. Those come down as CSV text files into a specific download folder. My Access database watches that folder, and whenever the files appear it imports them and processes the data. You could do something similar where your tablet or a small web script drops data in a shared location, and then Access picks it up and processes it on its loop. Or you could even write to a specific table that Access could process.

So the short version: Access can't directly receive an HTTP POST like a web server, but with the right setup you can still build a workflow that looks and feels like handling API calls.

Watching

Visual Studio is free, and you can use it to create an API application that retrieves info from Access.  You can then put the API app on your local IIS web server (which comes with Windows).  Your local users can then make API calls to retrieve info from Access.  So that's one way to do it if all your users are local.  To allow anyone on the Internet to make API calls to you, your API app and your database need to reside online with a web-hosting site like Winhost.  You can't put Access databases online, so you need to use SQL Server as your database instead.

Actually is achievable , I have implemented in the past something similar (actually I had it read data)
On the other hand it is generally accepted there are other more robust solutions but as always MS Access can do it