Learn German: Beeil dich, sonst kommen wir zu spät. - Hurry up, or else we will be late.

Yes! In German, the verb for to hurry is sich beeilen, which is a reflexive verb (literally meaning to hurry oneself). Since this is a command directed at one person informally, you use the reflexive pronoun for du, which is dich.

Why is the verb just beeil instead of beeilst?

This is an informal command (the imperative) for a single person. To make this command, you take the regular present tense du form (du beeilst) and drop both the pronoun du and the -st ending, leaving just beeil. You can sometimes add an -e (beeile), but dropping it is very common in everyday spoken German.

Why is the verb kommen before the subject wir in the second part of the sentence?

The word sonst (otherwise / or else) counts as the first position in its clause. In a regular German main clause, the verb must always take the second position. Because sonst is in position 1, the verb kommen must immediately follow it in position 2, pushing the subject wir to position 3.

Since this lesson is about the conjunction wenn, how could I rephrase this exact sentence using wenn?