I burned the bootloader in ATtiny45 with the Arduino tool.
- I want to know how much memory it has taken.
- Is this bootloader the same code of a bootloader used in the 328P or other chips?
- Can I see this code in any way, to know how it works?
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1) I want to know how much memory it has taken
Look to see how big the bootloader is. If it's a HEX file you will either want to load it into a HEX (Intel HEX, not hexadecimal representation) file editor, or convert it to binary with
$ avr-objcopy -I ihex <hex file> -O binary <bin file>
2) and if this bootloader is the same code of a bootloader used in the 328P or other chips
No, each chip requires its own special bootloader - simply because all chips are different: that's why they exist. If they were all the same there would only be one chip.
3) Can I see this code in any way, to know how it works ?
If it's open source and you download the bootloader from wherever it's stored (probably Github somewhere), then yes, you can. Of course, that also assumes that you would understand what you are seeing which, judging by this question, is not that likely.