I think this is the first command I've seen that has the verb at the end of the sentence. I don't understand why it isn't "Schauen nicht nach unten!" or "Schauen nach unten nicht!". And why is the verb "schauen", rather than "schau" or "schaut"? Thanks to anybody who can explain this. Maybe it's just colloquial speech and doesn't follow the typical pattern?
This is a kind of command that uses the infinitive -- and the infinitive always comes at the end.
Since infinitives don't change for person, you're not addressing anyone specifically -- it could be one person or many. So such commands with infinitive are most commonly used when you don't know in advance whom you are addressing: recipes in cookbooks or public signs, for example. But you can also use them when you're speaking to a specific person or people.
Schau! (to one person whom you know well), Schaut! (to multiple people whom you know well) or Schauen Sie! (to one or more people whom you do not know well) would also be possible, and would come at the beginning: Schau/Schaut/Schauen Sie nicht nach unten!
That sounds odd to me in English.
under is usually a preposition, followed by a noun, e.g. under the table, under the sea, under the chair.
Sometimes it's an adverb as part of a phrasal verb, e.g. he went under.
But there's no phrasal verb look under that I'm aware of.