Learn Russian: Позвони хоть раз в неделю.

Хоть means "at least" or "if only" in this context. While your current lesson covers даже ("even") to emphasize something surprising or extreme, хоть is used to lower expectations. It shows you are asking for the bare minimum: "Call at least once a week."

"Once a week" implies a repeated action. Why does the sentence use the perfective verb позвони instead of the imperfective звони?

You are right that repeated actions normally take the imperfective aspect. However, using the perfective позвони here makes the request feel like an emotional plea for a specific result. The speaker is focusing on the successful completion of that one single call per week, rather than just describing a regular ongoing routine.

Why do we need the preposition в before неделю?

In Russian, to express frequency like "per" or "a" in English (as in "once a week"), you use the preposition в followed by the accusative case. For example, "once a week" is раз в неделю, and "twice a month" would be два раза в месяц.

Could I say один раз instead of just раз?

Yes, you can perfectly well say один раз в неделю, but the word один (one) is usually dropped in everyday speech because раз on its own already means "one time". If you wanted to say "twice", you would have to specify the number: два раза.