I believe that as part of the init process, one of the first initialization schemes is systemd.
If you would like to control an LED with a GPIO output as soon as the systemd phase is initialized - well, it appears you are out of look. The GPIOs are initialized after the systemd phase. The earliest you will be able to send an output with GPIO is when it is initialized.
Alternatively, you could create an init.d script which would run as soon as the script is discovered, but that may happen even later in the process. Someone on the Raspberry Pi forums (https://www.raspberrypi.org/forums/viewtopic.php?f=44&t=24491) attempted to turn off the GPIO LEDs with an init.d script, but it appears to have not worked.
I believe it is possible to embed commands within GRUB to run as soon as GRUB is - however I'm afraid that the Pi does not utilize GRUB.
If you have experience with modifying the kernel, you could edit it - it runs before the Init process, but after the boot process.
You can read here (What is the boot sequence?) about the entire boot sequence, and you will see that certain files execute even before the kernels. They are binary files, and modification of them could be quite a challenge.
As for the shutdown LED, the system will unmount the devices and storage, meaning that you could make a script (it would have to be loaded into the RAM alongside the system) that will check when all processes except the main system and itself are ended, and that the storage is unmounted. However, you will need to make this script survive a shutdown command until a complete power halt.