I am confused by this one, since Schlaf is a noun (capitalized/non-conjugated), but "Sleep more" implies "(You should) sleep more", with 'sleep' as a verb.
How can a noun be used as a command like this? Shouldn't "Sleep more" be translated to "Schlafst (du) mehr"?
This is being used as the imperative form of the verb. You conjugate it based on the verb stem (remove the -en or -n, depending on what the dictionary form is).
Basic explanation: For imperative du, you use the verb stem. For imperative ihr (plural you), you use the verb stem + T For imperative Sie, you use the dictionary form and add "Sie" after the verb.
Example: schlafen (You) sleep! = Schaf! (Plural you) sleep! = Schalft! (Formal you) sleep! = Schlafen Sie
For more details see http://www.dartmouth.edu/~german/Grammatik/Imperative/Imperativ.html
It is capitalized because it is the first word of the sentence. It really is a verb here.
Because they're expecting a command. For commands you can either say "Schlaf mehr" or "Schlafen Sie mehr"
what's the object of this setence? I think it's "Sie" and you omit -e at the end?
Technically there is no object, but I would say the subject here is "Du", since this is an informal command. If it were formal, it would be "Schlafen Sie mehr." with the "Sie" explicitly included.
And if it were plural (ihr), it would be "Schlaft mehr" with a different ending.
There is no object. "Sleep"/"Schlafen" is intransitive.
"Sie" is only added for formal commands (e.g., "Schlafen Sie mehr"). It is not implied or left out here, and it is not the object of the sentence.