German

Would it not be,

Wir müssen um zu leben essen?

Modals bump the verb infinitive to the end?

They do, but not in this case - "Wir müssen essen" and "um zu leben" are two separate clauses, so the müssen will send the verb to the end of the first clause only, not to the end of the whole sentence.

The passive voice is when the action (the verb) is being done to the subject, rather than the subject doing it. For example, "ich beobachte die Lehrerin" is "I observe the teacher" (I, i.e. the subject, is doing the observing) and therefore in the active voice. "Ich werde (von der Lehrerin) beobachtet" is "I am observed (by the teacher)" - in this case, the subject is being observed. It's used when in English you'd say "I am ____" or "I am being ___".

You form the passive with the relevant form of werden and the past participle. So if it was "I was being observed", it would be "Ich wurde beobachtet" (as wurden is the imperfect form of werden).