Hello, yes you can buy an ESP32 chip and simply upload a new Arduino sketch (it instantly will work with the Arduino IDE, there’s not seperate bootloader required).

Ok.

No, you don’t need anything else… you can upload to your board any code with a simple FTDI programmer, if you connect TX-RX and RX-TX.
But for convenience, most people prefer to include a built-in programmer in their development boards (they often choose the CP2102 for the ESP32)…