Learn Farsi: لطفاً صبر کن.

The two little diagonal lines above the last letter are a special marker borrowed from Arabic called a tanvin. It tells you to add an "an" sound to the end of the word. In Farsi, you will see this mostly on adverbs like لطفاً (please) and حتماً (certainly).

Why is the word for "wait" made up of two words, صبر کن?

Farsi uses a lot of "compound verbs," which are formed by pairing a noun or adjective with a simple helper verb. Here, it combines صبر (patience) and کن (do). So to say "wait," you are literally telling someone to "do patience."

I learned that command verbs usually start with the prefix "be-". Why is it missing from کن here?

You are right that commands normally take a "be-" prefix. However, when the verb کردن (to do) is part of a compound verb like this one, Farsi speakers usually drop the "be-" prefix. Saying صبر کن is much more natural than saying صبر بکن.

Is صبر کن used for formal or informal situations?

This is informal. Because کن is the informal singular command form, you would only use this exact phrase with a close friend, a child, or a family member. If you need to be polite to a stranger, or if you are talking to more than one person, you would use the formal command form and say لطفاً صبر کنید.