Learn German: Muss der Chef heute früh kommen? - Does the boss have to come early today?

Because this is a yes/no question! In German, you form a yes/no question by putting the conjugated verb (muss) in the very first position, followed immediately by the subject (der Chef).

Why doesn't muss have an umlaut (ü) like its dictionary form müssen?

Modal verbs often change their main vowel for the singular pronouns (I, you, he/she/it). For müssen, the ü changes to a regular u for ich muss, du musst, and er/sie/es muss (der Chef is a masculine subject, so it uses the er form). The plural forms keep the umlaut.

Why is kommen at the very end of the sentence?

When you use a modal verb like müssen (to have to), the modal verb takes the main action spot in the sentence and pushes the second verb (kommen) to the very end. This is a very strict rule in German!

If the subject is der Chef (he), why doesn't kommen end in a -t like kommt?

Because the modal verb muss is already doing the job of matching the subject. In sentences with modal verbs, the second verb at the end of the sentence always stays in its raw dictionary form (the infinitive) and does not get conjugated.