Connections to what are one of many questions. Which Arduino model are you using as the programmer? Did you successfully compile and flash the “Arduino as ISP” sketch to that board being used as the programmer?
You do not need to change fuse settings in order to flash a bootloader. The Arduino IDE takes care of that for you when using the “flash bootloader” function.
Please attach a schematic of your 2560 target board. If you cannot attach it to a post, PM it to me and I’ll get it into the thread. A photo of your programmer to target board connections would be helpful as well.