Why is the value 0 for the Max_data_length of my tables in my database
Table size limits are affected by the OS and the file system.

From MySQL (5.6) documentation, Limits on Table Size:


  The effective maximum table size for MySQL databases is usually determined by operating system constraints on file sizes, not by MySQL internal limits. The following table lists some examples of operating system file-size limits. This is only a rough guide and is not intended to be definitive. For the most up-to-date information, be sure to check the documentation specific to your operating system. 


Operating System                      File-size Limit
-------------------------------------------------------------
Win32 w/ FAT/FAT32                    2GB/4GB
Win32 w/ NTFS                         2TB (possibly larger)
Linux 2.2-Intel 32-bit                2GB (LFS: 4GB)
Linux 2.4+  (using ext3 file system)  4TB
Solaris 9/10                          16TB
OS X w/ HFS+                          2TB


So there the problem lies. 

Solution:  


Take a backup.
Get another machine / VM with a 64-bit OS.
Install MySQL.
Restore your database there.
Profit ;)