How do I Reverse Firmware? What is firmware binary?
If I could, I would comment asking you to rephrase your question as I'm not sure what you want to know (file paths?).
As I'm not sure what can't be solved without some googling I'll give you a generic overview of the topics you mentioned. I suggest you to read all the links provided and update the question if you still have doubts.
In electronic systems and computing, firmware[a] is a type of software that provides control, monitoring and data manipulation of engineered products and systems. Typical examples of devices containing firmware are embedded systems (such as traffic lights, consumer appliances, remote controls and digital watches), computers, computer peripherals, mobile phones, and digital cameras. The firmware contained in these devices provides the low-level control program for the device.
Since it is a software running on some sort of hardware, it can be obtained in various ways: by either dumping the memory of the device or by downloading it from the vendor's site.
Once you have the binary file and you identify the architechture it is runs on you can use a disassembler to translate opcodes to assembly (which is a human readable rappresentation of machine language). Decompilers can be used to ease the process
In order to edit these images you just need an hexadecimal editor: programs such as IDA and radare2 can accomplish such task.
If you want to run the said firmware, you need an environment that supports the architechture on which it was running (an emulator or a virtual machine).