Welcome to LQ, raiput944!
The LED indicator on the computer chassis is independent of the external drive. That drive corresponds to the LED on the external drive enclosure. Sometimes when a drive is unmounted, there are a few transactions to be written to the drive or the drive journal. So you might see the light for a second after you issue umount. If the LED on the PC chassis is lit when you unmount, don't worry about it.
If the drive is making noises that's a bad sign. I would install "smartmontools" and display the SMART data with
smartctl -a /dev/sdb
or whichever drive it is. Then, run a test on the drive with the same program.
and scroll down to the examples.