Learn Swedish: Jag vill köpa en grön bil. - I want to buy a green car.

Because it describes the noun bil (car), which is an en-word (en bil). When an adjective describes a singular en-word, it stays in its base form. If you were describing an ett-word, like an apple (ett äpple), you would add a -t and say ett grönt äpple.

The English translation is "want to buy". Why is there no att (to) before köpa?

Vill (want) is a helper verb (modal verb). When you use it with another verb, you put the second verb straight into its dictionary form (infinitive) without using att. It works just like "can" or "must" in English: you say "I must buy", not "I must to buy".

Since this is happening now, why doesn't köpa end in -r?

When you chain two verbs together, only the first one gets conjugated to show the tense. Here, vill is already in the present tense, so the second verb (köpa) has to stay in its basic dictionary form (infinitive).

How is the k in köpa pronounced?

Because the k is followed by ö (which is a "soft" vowel in Swedish), it softens into a sound similar to the "sh" or "ch" in English. So, köpa sounds roughly like "shuh-pa".