Yo soy

Yo soy
 

I am checking out this new website, it says:

Yo = I / Me
Soy = I am / This is / Present

So I translated: Yo soy John to I am John.

I don't know why both yo and soy are used. It seems like then it should be: "I I am John".

I don't know why soy goes from "I am" and "This is", which are similar to "present"... Why would someone say "Present John"?

You are right that 'yo soy' don't both need to be said. If you do say that, you are giving emphasis to the subject pronoun 'I'.

soy = I am

They give 'this is' as a variant to accommodate the English 'This is John', when spoken by John.
'This is John' = 'Soy John' = 'I am John'

The English word 'present' is a formal response given by a student during roll call. It looks like they are suggesting that 'soy' is the Spanish equivalent.. Saying 'Presente' would be too formal a response, so pupils answer 'Sí, soy yo' (like saying 'Here' in English). They often shorten that response to just 'Sí'.

I don't know. It told me the correct answer was: Yo soy John. But there wasn't any context. It was just a sentence.

I am going to keep going to the next lesson and see what happens.

Beginning students are often taught that subject pronouns must accompany the conjugated verbs. Over time, you'll see that unnecessary pronouns are dropped.
(That said, Spanish has some redundancy allowance. Discovery awaits. ;) )