Hi all,
I don't want a solution, I just looking for the right way to implement something which I have never made before and I don't know its name....
It is something like port forwarding, rerouting, redirecting with some spoofing or proxy or ???

So actually I have a web server on a smart home device which can switch lights on/off, regulate temperature, dim lights ...
I have also a smartphone where a google app is installed which is connected to this web server and drives that unit.
What I want is to catch that traffic, and either modify the commands (arriving from phone) or send commands to the unit directly, without the phone.
This unit has an api with a relatively simple syntax (using both get and put), the response is a json "file" and I have a raspberry pi for this. But what is the tool to use (in perl/python/whatever)?
The pi should be seen as the web server from the phone.

I'd lean towards perl for this if you want a custom proxy, for authentication and to sanitize and validate any input on its way to your home device. CPAN modules to look for would be LWP::UserAgent, FCGI, and JSON. You'd needs a small web server for that to set up the FCGI socket that the perl script would then listen to. Requests would be processed and checked, and a JSON object built and passed to the home device inside with an HTTP or HTTPS call.

If you're only worried about authentication then even that might be overly complicated and so Squid might be enough. The main thing that I would worry about is having your home device sufficiently isolated on the LAN so that it only accepts access from the proxy.

Just plain port forwarding from an intermediate machine might be a bad idea if the forwarding proxy does no additiona authentication.

Does your device use HTTPS? Is it using a wired network connection or wifi?

authentication is not an issue. This is only available on the local net and this web server has no any user/password to check.