External Hard-disk showing Input/Output error
If Windows is having trouble opening various folders and is causing your drive to freeze, it suggests that the file system is corrupted or that the disk itself is failing. The first thing you should do is run chkdsk on the drive from a Windows system to correct any errors with the NTFS file system. If you still have trouble, I suspect that there's little you can do.

As for mounting it on the Mac, understand that OS X mounts NTFS file systems in read-only mode. As such, you'll be able to copy important data off of the drive, but you won't be able to update it or write new data to it.

Repairing the drive in Disk Utility might work, but I advise against it. As for it being unmounted, that is always going to be the case. One cannot repair a volume while it's mounted, in the same manner that one cannot chkdsk /f a drive under Windows without forcing the drive to be unmounted (or reboot, which does the same thing). Importantly, though, if you want to repair NTFS, you're best off doing it with Windows.