Hi,
1. Suppose FCCU is initialized in Bootloader,
You better ask you bootloader vendor what you have in bootloader.
does application needs to take care of anything? something like petting watchdog?
This is fully application dependent. You must know if you require safety countermeasures or not in your application.
2. Is FCCU a one time initialization component? Something like SBC?
Since you didn't share about which microcontroller you are writing I will answer generally.
FCCU after power on reset is in default state. The state of FCCU registers depends on type of reset. Destructive reset also destroys content of FCCU. Also BIST destroy content of FCCU.
So generally it is recommended to perform FCCU initialization, fault reading, fault clearing and fault analyzes after Power on reset and also after fault state. If you do not require safety in your application you can just configure FCCU to ignore all incoming faults.
3. What happens if FCCU is initialized in both bootloader as well as in application?
Nothing. It is common peripheral and you will just overwrite its registers. Until FCCU leave configuration state you will go with actual registers configuration.
Peter