The solution to fix your external hard drive in mac are as follow:
Formatting:
1.Make a backup of your data on a windows pc/mac.
2. Format your drive with mac disk utility tool in Macintosh hd ->applications -> utilities -> disk utility.
Now, select your hard drive and go to erase tab and select "Erase" and format it to your required file format system.
Formatting:
1.Make a backup of your data on a windows pc/mac.
2. Format your drive with mac disk utility tool in Macintosh hd ->applications -> utilities -> disk utility.
Now, select your hard drive and go to erase tab and select "Erase" and format it to your required file format system.
Self eject solution:
If you have problems with your external hard drives ejecting itself after few seconds which only gets fixed when you restart then make sure when you are running your hard drive on mac.
Make sure you have unchecked "Put the hard disk(s) to sleep when possible" in the battery tab. (Make sure you recheck it after you done by ejecting your HDD)
Other Solutions:
1.Check the Finder's -> Preferences and General (Tab) -> put a check mark in "External disks" (on the desktop)
2. Go to Macintosh hd ->applications -> utilities -> disk utility if you see your your external hard drive. Then the drive is not dead.
Select the drive and unmount it so the external hard drive will disapear from desktop and side bar.
Now to get it back the HDD drive on side bar and desktop select mount. But make sure to "EJECT" it before disconnecting.
If you still have problem please take it to a apple mac store or hard drive manufacturer service center.
If mac store doesn't help put the hard drive in a zipped locked air tight bag for 2-3 days and try copying the files by connecting it to your computer you may be able retrieve some data.
You can also try using the NTFS3G (Free version) software if you are using a dos formatted hard drive to copy files from a mac to windows file formatted hard drive but it would still may give hiccups if you are copying files above 4 gb.
Bonus:
You use Macdrive software to read and write mac formatted hard drives to be read on windows just like any ordinary pen drive.
You can also use a 'HFS Explorer' which is a free read only software to read mac formatted hard drives on pc and also cdr and dmg files on windows.