You're close! Here are a couple of minor changes.
1. Don't forget a subject in your sentences! Ask yourself, "Who is protecting the animals?" I'll assume that you're talking about you. The first sentence would then read, "I help to protect extinct animals." Okay, now that we fixed the issue of a missing subject, there's another one I want to point out (see below).
2. Currently, the way most of the sentences are written create two verbs, "(to) help" and "(to) protect." Choose whichever one you want to use, but not both. Here's a revision of the first sentence: "I help protect animals from going extinct," or, "I protect animals from going extinct." You'll notice I added the words, "from going." See the next point for the explanation.
3. The sentence would be grammatically correct if you wrote, "I help protect extinct animals," but the word "extinct" is being used in a way that might confuse readers. That is because animals that are extinct are...extinct! You can't protect an animal that is already extinct (although I wish we could). What I think you might be trying to say is, "I help protect animals from going extinct." "From going" indicates that you're trying to prevent the animals from becoming extinct.
Alright, now try these corrections for the rest of your sentences. Below are the answers:
1. I help protect animals from going extinct.
2. I help protect animals from becoming extinct.
3. I protect animals from becoming extinct.
1. It helps you avoid skin cancer.
2. It helps you avoid getting skin cancer. (You can use "getting," but it's unnecessary)
3. This sentence is incorrect. If you're talking about a product that helps with preventing skin cancer (e.g., sunscreen), it's better to use sentence 1 or 2. The sunscreen itself is not avoiding getting skin cancer; rather, the sunscreen helps YOU not get skin cancer.
1. It helps you prevent skin cancer.
2. It helps you prevent from getting skin cancer.
3. Sunscreen prevents you from getting skin cancer.