Yes NTFS read/write is supported on OSMC.
Keep in mind that if you are trying to power the drive directly from the Pi 2 you will need to enable max_usb_current=1 in config.txt and have a good power adaptor. Not all drives can be successfully powered from a Pi so you may need an external power adaptor for the drive.
Yes to both of those.
To disable internet access the easiest way would be to use a Static IP configuration instead of DHCP and simply set the Default gateway deliberately to an IP address other than your router - eg an address not in use by any device.