Learn Hardcore Japanese: watasi ha mada syukudai wo dasite imasen.

まだ means “not yet” when used with negative verbs. It indicates that the action hasn’t occurred up to now but is expected or planned.
Example: まだ宿題を出していません = “I haven’t handed in my homework yet.”

Why is the verb 出す in the form 出していません instead of just 出しません?

The structure ～ている + negative expresses that an action or its resulting state continues up to now.

出していません = “has not been turned in (and still hasn’t)”
出しません would mean “I will not turn in” or a refusal, not “haven’t turned in yet.”

What nuance does the ～ている form (here 出している) convey?

In 宿題を出している:

Progressive: the action is ongoing (“in the process of handing in”) – less common here.
Result state: the action has occurred and its result remains (e.g. “I have handed in”).

In the negative (出していません), it emphasizes “I have not yet reached the state of having handed in.”

Why is the negative ending いません and not いない?

いません is the polite present negative form of いる.

いない is the plain (casual) present negative.

For polite speech, you replace いる with いません in ～ている to form ～ていません for “is/has not …ing.”

What’s the difference between 出していません and 出してない?

They mean the same (“haven’t turned in / haven’t submitted”) but differ in register:

出していません: polite speech
出してない: casual/plain speech

What is the function of the particle を after 宿題?

を marks the direct object of a transitive verb. Here 宿題を出す means “to submit (the) homework,” so 宿題 is what you submit.

What does the verb phrase 宿題を出す mean exactly? Can 出す have other meanings?

宿題を出す typically means “to hand in / to submit homework.”
出す alone can also mean “to take something out,” “to publish,” “to serve,” etc. Context and the direct object determine the exact meaning.

Why is 私 marked with は rather than が in 私はまだ宿題を出していません?

は is the topic marker and sets 私 (“I”) as the topic of the sentence. Using が would emphasize 私 as the subject among others, but learners often use は for self-introduction of topics, especially in statements like “As for me…”

Can 私は be omitted here?

Yes. Japanese often omits subjects when they are clear from context. So まだ宿題を出していません is perfectly natural if it’s obvious you’re talking about yourself.

Could you say まだ宿題を出しません instead of 出していません?

No. まだ宿題を出しません would imply you are refusing or simply not planning to hand it in. To express “haven’t handed in yet,” you need the ～ている form: 出していません.