As this varies and can change, the best is to check at IATA - I added the link below.
We don't speak Spanish. All the destinations we travelled to, it worked with English, some gestures and a smile. HOWEVER, it is true that many people don't speak english and that they appreciate you trying.
So I encourage for you to learn Spanish, but you will get around without.
Yes, it is real- while we were ok, we saw others that really weren't. The best way to deal with it is time. Adapt slowly over days to increasing height. Arrange your schedule accordingly by going a little higher every day. During the days at high height drink a lot of water. I describe how we did it in more detail in my article about San Pedro Atacama.
The destination we travelled to in Argentina, Chile and Ecuador are safe.
We acted wisely and followed instructions where to go and where not to go.
Mexico is a bit different - I will share my thoughts in the Mexican section.
Mostly you need Yellow Fever, Hepatitis A, Poliomyelitis, Diphteria - Tetanus - Pertussis, Measles - Mumps - Rubella, Chicken Pox
Check every country on bellow link.
Argentina: Best is end of November to March (so Argentinian spring to autumn). Particulary Patagonia gets cold and hotels close after April/May.
Chile: Best is end of November to March (so Chilenean spring to autumn).
Mexico: November to March (Dry season) - better as early as you can as it gets really really hot.
Galapagos: Really depends on the wildlife you would like to see. December to May is a great time for hatching, lush nature and it is hot hot hot beach weather. However, in August and September, when it is colder, you have to opportunity to see more big fish and whales.