Q: Can I turn off terminal case sensitivity As above can I turn Case Sensitivity off for terminal in linux?

A: No. Case sensitivity is not a property of the terminal. It's not even a property of the shell. When it comes to file names, it's a property of the filesystem: you can have a file called foo and a file called FOO in the same directory, and they're different files, just like a file called foo and a file called bar are different files. It's also a property of individual programs: for example ls -a and ls -A mean different things.
Unix generally uses lowercase all around anyway. So most of the time you just need to refrain from using the Shift key.
When you mount external filesystems that some OSes treat as case-insensitive, you can control whether Linux should treat them as case-insensitive too, by specifying the right option when mounting (see the mount(8) manual page). I think this is usually done by default for fat, hfs and ntfs.
If you use zsh, you can configure it for case insensitive completion in various ways (for example, if you type f and there is no file called f* but a files called FOOBAR and FOOBAZ, the f would change to FOOBA). Run compinstall to configure the simpler aspects of case-insensitive completion, and read zsh tutorial or the reference manual to find more options.

A: No you can not since filenames and programs then could be duplicates of eachother. The structure of Linux and the filesystem would not allow for proper execution.
For example if the /bin would contain mv and MV, executing mv would execute them both.
