I've been working on a school project that consists into making a smart light socket. I want to make an app which will allow the user to control many of them, like switching on and off, controlling the light intensity and other functions.
So, I guess the most important for me now is to know if I can connect each ESP-01 to the Internet and control them individually.
Your question has many topics to take into consideration. Using an ESP-01 to control a mains powered device from a mobile app via the internet has a lot of pieces to integrate into one project. It can be done, but if you are asking this question, it may be a bit daunting if your experience is limited.
If you are just getting started, you might consider looking into existing projects like zigbee2mqtt and commercially available smart home lighting like that from IKEA instead of starting from scratch. It will get you to your end result a lot faster and you'll have more support in getting it to work.
