Learn German: Ich habe ein Bier bestellt.

The verb here is bestellen. It starts with the inseparable prefix be-. When a verb starts with an inseparable prefix (like be-, emp-, ent-, er-, ver-, or zer-), it does not get a ge- added to the front when forming the past participle.

Why is bestellt at the very end of the sentence?

This is the standard word order for the spoken past tense (the Perfekt) in German. The helping verb (habe) takes the second position in the sentence, and the past participle (bestellt) is pushed all the way to the end, forming a frame around the rest of the sentence.

Why do we use ein Bier here instead of einen Bier?

The word Bier is a neuter noun (das Bier). Because it is the thing being ordered, it is the direct object (accusative case). For neuter nouns, the word for a or an stays ein in the accusative case. You would only use einen for masculine nouns.

Can this sentence also translate to I have ordered a beer?

Yes, absolutely. German does not make a strict distinction between I ordered (simple past) and I have ordered (present perfect) like English does. The Perfekt tense used here is the most common way to talk about the past in everyday spoken German.