Your system will not work as drawn, but it can kill you if you do not have experience working with mains power. NEVER connect any portion of the mains circuit to an Arduino. Simple solution get a small DC wall wart that puts out 5V DC, connect that output to a port pin and the ground pin of the Arduino, plug it into the mains circuit. It may be a bit sluggish depending on the design of the wall wart but you will live many happy days without becoming a crispy critter.
It doesn't make any sense.
Either you disconnect the switch from mains and wire it directly to arduino which is controlling the relay according to state of that switch (or other triggers)
or
You buy a $10 smart switch, like Shelly, and you have safe and approved hardware.
A wall wart is similar to a phone charger. What does the switch turn on, plug the wall wart into that. When the switch is on the wall wart will be outputing voltage to your arduino.
Start reading about how AC works, and how switches, overhead lights and wall sockets are wired. Also read up on safety measures to take when working on live AC. Once you understand all of that, come back to this question and reformulate it based on what you've learned. You will then also recognize that the schematic you drew in post 1 doesn't make any sense whatsoever.
While you're studying, do as the people above told you and buy a ready made remote controlled switch and ask a qualified electrician to install it for you. Don't mess with the live AC wiring in your home without knowing what you're doing. You'll put yourself at risk and everyone else in this house, as well as future owners, and insurance may not cover the damages if your house burns down because you messed with the wiring. It's just not worth it.
So you would like to know whether a mains circuit is on which is attached to a lamp?
You would like to know if the lamp is on, and act on that from the Arduino?
Is this correct?
If so, you might use a photoresistor (modules are even easier than making your own voltage divider for this), then based on the light level from the lamp, use the Arduino to switch the mains power with a device built for that.
There are several ways of sensing if lights are switched on, there are even $1 voltage sensing modules for that. But If OP wants to control the lights also with a relay, it makes no sense to make two parallel switching that are never in sync.