Why is this sentence: "Additional nine features were added…" incorrect?

It has to do with the order of the adjectives.

For example, consider this sentence:

Happy nine men walk into a bar.

Both nine and happy are adjectives, but we are really intending nine to describe the happy men, not happy describing the nine men. I don't know if there's a specific term for this, but certain adjectives, like numbers, get special treatment in this way.

This is why the phrase:

Nine additional features....

is the correct phrase.

I think the main problem with Additional nine features were added has to do with adjective order. As you pointed out, you can say nine additional features (because that's in the right order). *Additional nine features is in the wrong order and is therefore incorrect.

Ordinarily, your friend would have a point: You generally can't use the indefinite article with plural nouns (*a cars, *a children). However, this is an interesting case. According to Dictionary.com, the article a can be used

5. indefinitely or nonspecifically (used with adjectives expressing number): a great many years; a few stars.

(Thanks to this question for help with that.)

Since additional is an adjective expressing number, it can take the indefinite article and come before nine. Otherwise, the construction is incorrect.