Today I was watchingtched a short documentary about the nature reserve Massai Mara, in Kenya.

"was watching" is only used when you are going to say that something happened during the "watching". For example, "I was watching a short documentary, when suddenly a bird flew into my window!". In your example, you just want to say that you watched a documentary, so just say: "I watched a short documentary..."

There wasere a lot of animals: elephants, giraffes, buffaloes, hippos, etc.

Use "were" for plurals. Example: There were a lot of animals.
Use "was" for a singular item. Example. There was an animal.

The tribespeople said that before they killed animals forto protected their families and houses, but now, they protected animals because they understooand the fragility and importance of the environment.

The documentary also showintroduced a foundation striving for the recovery of certain trees and ithey explained the importance aboutof donations.

Is the foundation an organization in this context? It's better to say the documentary "introduced the foundation" instead of "showed the foundation"
The documentary is one thing, so you say "It explained the importance ..."

The camera shots were excellent.

You can ignore this advice to me, but I think "shots" is a little ambiguous. "Shots" is correct but for a general audience it is not specific enough in my opinion.