Мне нужно сдать отчёт директору до обеда.

Yes. Мне нужно... is a very common Russian way to say I need to..., and it’s built as:

• мне = to me (dative case)
• нужно = necessary / needed (a “category of state” word)
• • an infinitive: сдать (to submit/hand in)

Russian often expresses “need” impersonally (it is necessary for me), so Я is not required here.

Мне is the dative singular form of я.

• Nominative: я
• Dative: мне

You can recognize it because нужно/надо/можно/нельзя frequently take a dative experiencer: мне нужно, ему нельзя, нам можно, etc.

In this sentence нужно functions as a predicative word (often called a “category of state” word). It behaves like a predicate meaning it is necessary. It doesn’t agree with мне (no gender/number agreement), which is why it stays нужно.

Сдать is perfective and focuses on completing the action: to hand in (and have it done)—especially natural with a deadline (до обеда).

• Мне нужно сдать отчёт... = I need to submit it (get it done).
• Мне нужно сдавать отчёт... would sound unusual here; imperfective сдавать would fit repeated/ongoing situations, e.g. Мне нужно сдавать отчёты каждый месяц (I need to submit reports every month).

Сдать has several common meanings, and context decides:

• сдать отчёт = submit/hand in a report
• сдать экзамен = pass an exam (successfully)
• сдать квартиру = rent out an apartment
• сдать вещи = turn items in (e.g., to a cloakroom)

With отчёт, the meaning is clearly submit/hand in.

Отчёт is the direct object of сдать, so it’s in the accusative case. For many inanimate masculine nouns, nominative and accusative look the same:

• Nominative: отчёт
• Accusative (inanimate): отчёт

Директору is the indirect object: the recipient of the report (to the director). Russian often uses dative without a preposition to show the recipient:

• сдать отчёт директору = submit a report to the director

Not in this meaning.

• к директору means to the director’s office / to the director (as a destination) and is used with motion/going: пойти к директору (to go to the director).
• For giving/submitting to someone, Russian typically uses plain dative: директору.

You can combine them if you explicitly include the motion: Мне нужно пойти к директору и сдать ему отчёт.

До means until / by (no later than) and requires the genitive case.

• обед (nominative) = lunch
• обеда (genitive) after до

So до обеда = before lunch / by lunchtime (deadline no later than lunch).

They’re close but not identical:

• до обеда = deadline: any time before lunch; not later than lunch
• перед обедом = right before lunch (closer in time)
• к обеду = by lunchtime / for lunchtime (prepared to be ready at that time)

In your sentence, до обеда emphasizes “no later than lunch.”

Yes, word order is flexible, and changes what’s emphasized:

• Мне нужно сдать отчёт директору до обеда. (neutral)
• До обеда мне нужно сдать отчёт директору. (emphasizes the deadline)
• Директору мне нужно сдать отчёт до обеда. (emphasizes the recipient)

The core grammar stays the same because the cases mark the roles.