What are the standard ATC light signals and emergency messages? Apart from 'mayday' which other common emergency messages are used? Is there any regulation regarding them?

Any other light are used by ATC than these? : https://learntofly.ca/wp-content/uploads/2010/11/ATC-Light-Gun-Signals.gif

Is it the same Emergency messages and  Light signals used worldwide or are they different US-Europe ?
Those signals are regulated by ICAO Annex 2 rule of the air:
https://www.icao.int/Meetings/anconf12/Document%20Archive/an02_cons%5B1%5D.pdf

Therefore international.Some other ground signals are indicated there but as far as light signals the ones you showed are the only ones.