Do you think that this implementation can be done?
Yes, but...
Currently I sent a string message from the webpage (using values from a data base created on Xampp-phpMyAdmin), then Arduino substring the message and turn on or off a led.
Currently you make a GET request, using some data. You don't send a string to a server.
Have you enabled Serial output from the Arduino as server to see what it is doing when you do things from the web browser?
You can have the browser, through the PHP script, issue a different GET request. To satisfy that one, the Arduino will return some data, not just toggle LEDs.
There are two problems with this. The first is that we can't see your code to tell how to integrate it. The second is that the data is pulled by the client, not pushed by the Arduino-as-client. If the web page is supposed to be showing anything like real-time data from the Arduino, it needs to ask for that data fairly often.
There are meta tags that can be put in the html page that the browser is showing that tell the browser that it needs to fetch the data frequently.
Of course, the browser will then often ask the Arduino for the same data it got last time.