Citizens of the US, Canada, the EU/Schengen, UK, Japan, South Korea, Australia and most of South America need no visa for stays up to 180 days. Russia, Ukraine and Turkey use the SAE electronic permit. Everyone else needs a consular visa — unless they hold a valid US, Canada, UK, Japan or Schengen visa.
Yes. Any nationality holding a valid US visa (or Canada, UK, Japan or Schengen) can enter Mexico visa-free for up to 180 days, even if their country normally needs a Mexican visa.
The SAE is an online entry authorization for citizens of Russia, Ukraine and Turkey, issued in minutes for a single air entry — an alternative to a consular visa.