Will multiple C Models work separately?

Yes they will work without any interference.

Can I add an additional Transmitter button or Receiver to my current doorbell?

Each C Model is a standalone unit and are sold with unique frequencies. Therefore an additional Transmitter or Receiver cannot be added. For expandable models you should look to purchase the STARPOINT series here: http://www.amazon.com/gp/dp/B00LFATHKS/

It appears one of my SadoTech Model C door Transmitters has gone bad, can I buy just a Transmitter?

Unfortunately for the C Models, each unit has their own unique frequencies and therefore you cannot replace just the Transmitter.