Why is my Mac able to write to my NTFS hard drive? My question is one of confusion.  All over the internet I have seen people looking for the ability to use a Mac to write to NTFS, or people formatting drives to FAT32 so that their Mac can share a storage drive with a PC.  

I am experiencing the opposite effect.  

I recently hooked up a Western Digital (WD) My Book 3 Terabyte drive to my network.  I connected both my PC and my Macbook Pro to it.  The Mac put a bunch of hidden folders on the drive, and my PC added it's own shared files.  The drive, from the perspective of the PC says the drive file format is NTFS.  I am able to access the shared drive as a Guest, from my Mac, and I can view all the files, add files (I added a picture) and pull music off the drive, and play it.  

I don't have a problem with this, but I'm wondering how this is possible?  

I have made 1 attempt to back-up on the network drive using Time Machine.  It was too slow over the wi-fi so I canceled, but it didn't come up with any pop-ups that said the back-up was failing.  

Because it's a network drive, is there some kind of conversion going on?  I haven't installed any programs to write to NTFS on my Mac.  

I would also like to know if I am damaging the Network drive in any way by using both the MAC and PC on it.  

Note:  My MacBook Pro does not see the Network drive as a Hard Drive, and I cannot use the Disc Utility to format it.  It only sees it as a shared drive in the Network.
Over the network it does not matter what file system is used on the hardware drive, because the computer hosting the drive (making it available through the network) will access it.  Your Mac will just make generalized requests over the network for files, folders, etc. and the host will access the file system and serve the files. Network requests are standardized and the host answers them and converts between those and the actual file system on the hardware. 

What you were reading about not being able to write to NTFS, was people who either had a partition with NTFS on their native HD in the Mac computer or who were attaching USB drives.  In both these cases, the Mac has to access (and possibly modify) the file system on drive directly (without an intermediate agent) and needs to be able to deal with the specifics of the file system directly.

And no, there is no danger of damage (well, not unless you or the Mac intentionally delete files or move folders that are needed otherwise).