Learn Dutch: Ik koop een oranje jas. - I am buying an orange coat.

Yes, jas is a de word (de jas). Usually, when you have een + adjective + de word, the adjective gets an extra -e (like een groene jas). However, adjectives that already end in a vowel, such as oranje (orange) and roze (pink), are exceptions. They never get an extra -e added to them.

Why is "I am buying" translated simply as Ik koop?

Dutch generally doesn't use the "am doing something" structure that English has. The simple present tense verb koop covers both "buy" and "am buying".

Does the word een change depending on whether it comes before a de word or a het word?

No, een (meaning "a" or "an") always stays exactly the same, whether it's used with a de word like jas or a het word like boek.