Learn German: In Ordnung, ich mache das. - All right, I will do that.

Yes, literally it translates to "in order". In German, this is a very common set phrase used to say "all right", "okay", or "fine" when you are agreeing to something or confirming that everything is good.

The translation says "I will do that", but ich mache is present tense. Why isn't there a future tense word?

In German, it is perfectly normal and very common to use the present tense to talk about the future, especially when the context makes it obvious. While German does have a specific future tense, native speakers usually just say ich mache das (literally "I do that") to mean "I will do that".

I learned that das means "the" for neuter nouns. Why does it mean "that" here?

The word das is very flexible! Besides being the article "the", it is also widely used as a pronoun meaning "that" or "this". In this sentence, it stands on its own to refer to whatever task or action was just discussed.

Does the phrase In Ordnung at the beginning change the word order of the rest of the sentence?

No, it doesn't. Because In Ordnung acts as an introductory phrase separated by a comma, it sits outside the main sentence structure. The main part follows the standard word order you learn early on: subject (ich), verb (mache), and then the object (das).