The three red oval items with the sawtooth edges and eagle design in your final photograph are Mexico registered letter seals. In the literature these are known as "Sunburst Seals" because of their shape.
These were used at most Mexico post offices between 1913 and 1965. They were applied by the postal clerk when the letter was submitted for registration, usually on the reverse to close the envelope flap and secure the contents. Prior to 1913, Mexico used wax seals but as registered mail became more common, the wax seal process was too time-consuming.
Between 1913 and about 1933, most Sunburst seals were blue, and after 1933 they were red. There is one variety that was printed/embossed in green. There are many major and minor varieties.
MEPSI published a monograph about these which can occasionally be found on eBay