Learn Russian: Из-за тебя нас задерживают!

Потому что translates to 'because' and must be followed by a full clause (a mini-sentence with its own subject and verb). To say 'because of' followed by just a noun or pronoun, you need a preposition. Here, the compound preposition из-за is used to show a negative cause or fault. It always takes the Genitive case, which turns ты into тебя.

There is no word for 'they' in the Russian sentence. Why does the translation say 'They are delaying us'?

Russian often leaves out the pronoun они (they) when an action is done by unspecified people, like authorities or staff. Using the 3rd person plural verb задерживают without a subject is a common way to express 'They are delaying us' or the passive idea 'We are being delayed'.

The verb is задерживают. Why use the imperfective aspect here?

The imperfective verb задерживать is used because the delay is an ongoing action happening right at this moment. They are currently in the process of holding us up.

Could we put из-за тебя at the end of the sentence?

Yes, the grammar is perfectly fine if you say Нас задерживают из-за тебя! However, Russian uses word order to show what is most important. Putting Из-за тебя at the very beginning emphasizes the blame: 'It is your fault that we are being delayed!'