Much better.You need battery ground connected to arduino ground.
I need to look up TSOP34856 again to see what it puts out.
Looks like you want to know if any of the three devices are active, you turn on the Hit light?Connect them like this.
We could have resolved this days ago if you had shown this kind of picture to start.
So wait, there's a route on the Arduino board from the digital pins to the ground pins?
"if I connect a data pin without a common ground to the Arduino, where will the current come out?"Exactly! You need the ground connection to complete the electrical loop.