I replied to this, too, but nigelc obviously has more pull with SCF, and overrode my contribution

As he says, the cut in half stamps are Telegraphs, and they were applied to the telegraph forms so that the top half of the stamp was returned to the sender. Here is a complete unused copy of a 1 Anna:

Incidentally, you might like to check the watermarks on your three Cochin stamps. The normal watermark is an upright small umbrella. A
very few inverted watermarks are known (these stamps were printed by Perkins, Bacon, who did the Penny Black, and were usually pretty careful) and are well worth having.