Updated simplified post here.
Strangely, when I plugged in my Seagate drive to Mac, it was able to detect it and read and write effortlessly. But after a few days, it showed it could only read the drive and not write to it. It was very strange and I started to look for options since I was planning to use this drive as Backup and was intending to write heavily to it.
Mac OS X has limited support for writing to NTFS file format, but because of limited support this feature is hidden. I found a script which used this feature to enable you to write to your disk, but this had its own limitation.
Using this script I was able to write to my drive but soon I found it corrupted my files and made them inaccessible. Frustrated I resolved to Google search a solution again till I stumbled across Seagate site. They have a NTFS support for Mac through Paragon driver which typically you have to pay for but is FREE for Seagate customers. Installation was seamless and after I restart, I was able to use my drive smoothly without any further glitches. Hopefully this post should help people going through similar experience.
PS - (From Appy's comment below) Check if your HDD came with preloaded NTFS for Mac driver