There is also this button. I'm not sure what it does if pressed and released. Does it hold its new state or does it just create a contact when pressed only?
The first one looks like a normal momentary microswitch. The second looks like a momentary button as well. Neither of them hold their state. You can check this using a multimeter.
I presume that one of the buttons is the reset button, and the other one is the programming button, connected to GPIO0:
That being said, it looks like a very convoluted and cumbersome setup. For just $4, you can get a WeMos D1 mini or similar board that packs everything (USB interface, voltage regulator, programming circuitry, reset button ...) on a single PCB. On top of that, it breaks out all usable GPIO pins of the ESP8266, and you don't have to press any buttons to upload code to it.
@PieterP, thank you for the clarification and advice. It is very helpful. I will definitely consider purchasing a WEMOS D1 Mini but for now, i only have an ESP-01 to work with. You have a great tutorial on the ESP-8266 and i'm going through your tutorial page by page: A Beginner's Guide to the ESP8266 to try and understand how to connect the ESP-01 and program it with Arduino IDE.
@Paul__B, thank you for the links but i only have some experience working with the Arduino UNO R3. The ESP8266 is still very new to me. I have an ESP-01 at hand and i'm trying to get things to work on a basic level before controlling a relay. I guess you could say that it's like a... trial by fire? :o
Well, the modules I cited make it perfectly easy to program and use the ESP-01, so that's what I would recommend.
While you are at it, (the modules from eBay take a while to arrive,) get a few more ESP-01s. Generally about $2 each though the D1 Mini is not a lot more (about $3), also dead easy (physically) to program and also has relay modules to match. ESP-01s will do most of the jobs you need.