USB and Thunderbolt both face issues with Energy Saver, and drives are best in their own external power supply (not supplied by the computer case) with the appropriate firmware for the OS:
USB/Thunderbolt & Energy Saver/Sleep/powe… - Apple Community
ExFAT and FAT32 are not Mac bootable.
NTFS is not Mac writable without extra software like NTFS MacFuse
Block sizes differ.
If you are going to share crossplatform data, read this tip:
How to format a drive, or disc for maximu… - Apple Community
Older drives use one of the following to diagnose more carefully:
In MacOS http://www.binaryfruit.com/ DriveDX
In Linux or Windows https://www.hdsentinel.com/
SMART errors indicate a drive is past its prime and probably ready to put to pasture.
Recovering data from Macs - Apple Community can help you recover items in Mac OS, although for really hard to read data, take it to a professional. If the data is worth thousands of dollars there is http://www.drivesavers.com/ If they can't recover it, no one can.
If the drive is readable, and just is slow mounting, make sure no volume is over 85% full.