Мне нужно дописать отчёт до обеда, а потом доесть суп.

Because нужно does not work like an ordinary verb meaning I need.

Russian often expresses this idea with a structure like:

• мне нужно... = I need to...
• literally, something like to me it is necessary...

So мне is in the dative case, because it marks the person for whom something is necessary.

Compare:

• Мне нужно уйти. = I need to leave.
• Тебе нужно отдохнуть. = You need to rest.
• Нам нужно поговорить. = We need to talk.

If you want to say I need with a noun, Russian also often uses мне нужен / нужна / нужно / нужны:

• Мне нужен отчёт. = I need the report.
• Мне нужна помощь. = I need help.

So in your sentence, мне нужно дописать... means I need to finish writing...

Here нужно means it is necessary or more naturally need to.

In everyday English, we translate:

• Мне нужно дописать отчёт as I need to finish writing the report

It is a very common and neutral way to express necessity.

A few related words:

• нужно = necessary / need to
• надо = need to / have to, often a bit more conversational
• необходимо = necessary, more formal

In many situations, мне нужно and мне надо are very close:

• Мне нужно дописать отчёт.
• Мне надо дописать отчёт.

Both are natural.

Дописать means to finish writing something that has already been started.

This is different from:

• писать = to write, be writing
• написать = to write something, to complete writing it
• дописать = to finish writing the rest of something

So:

• писать отчёт = to write a report / be writing a report
• написать отчёт = to write a report, complete it
• дописать отчёт = to finish writing the report, add what is still missing

The prefix до- often gives the idea to finish something up, to do until the end, or to complete what remains.

So this sentence suggests the speaker has already started the report and still needs to finish it.

Yes, very similar.

In both verbs, до- gives the sense of finishing something that is already in progress or doing it to the end.

• дописать отчёт = finish writing the report
• доесть суп = finish eating the soup

So the pattern is:

• something has already been started
• some part remains
• the speaker wants to complete it

More examples:

• дочитать книгу = finish reading the book
• доделать работу = finish doing the work
• досмотреть фильм = finish watching the film

This is a very useful prefix in Russian.

Отчёт is in the accusative case here, because it is the direct object of дописать.

The basic dictionary form is отчёт, and for an inanimate masculine noun like this, nominative and accusative singular look the same:

• nominative: отчёт
• accusative: отчёт

So:

• Я читаю отчёт.
• Мне нужно дописать отчёт.

Both use the accusative, but the form does not change because the noun is masculine singular and inanimate.

Here до means before or more literally up to.

• до обеда = before lunch / by lunchtime

The preposition до requires the genitive case, so:

• обед becomes обеда

Other examples:

• до вечера = before evening
• до завтра = before tomorrow
• до конца недели = before the end of the week

In this sentence, Мне нужно дописать отчёт до обеда means the report must be finished before lunch.

No. They just happen to look similar.

These are two different things:

1. дописать
   Here до- is a verbal prefix attached to the verb.

2. до обеда
   Here до is a separate preposition meaning before / up to.

So:

• дописать is one word, a verb
• до обеда is two words, a preposition plus a noun phrase

They are unrelated in grammar, even though they look alike.

потом means then / afterwards / later.

So:

• а потом доесть суп = and then / and after that finish the soup

The conjunction а often connects two parts of a sentence with a slight contrast, shift, or change of topic. It is often more natural than и when you move from one action to the next.

Here the idea is something like:

• first one thing
• then another thing

So а потом sounds very natural.

Compare:

• Мне нужно дописать отчёт, а потом доесть суп. = I need to finish the report, and then finish the soup.
• Мне нужно дописать отчёт и доесть суп. = I need to finish the report and finish the soup.

The version with а потом emphasizes the sequence more clearly.

Because they depend on нужно.

After мне нужно, Russian normally uses an infinitive:

• Мне нужно уйти. = I need to leave.
• Мне нужно позвонить. = I need to call.
• Мне нужно дописать отчёт. = I need to finish writing the report.

In your sentence, the second infinitive is understood as part of the same idea:

• Мне нужно дописать отчёт до обеда, а потом доесть суп.

This means:

• I need to finish the report before lunch, and then finish the soup.

So both actions are things the speaker needs to do.

Суп is also in the accusative case, because it is the direct object of доесть.

Like отчёт, суп is masculine singular and inanimate, so the accusative form is the same as the nominative:

• nominative: суп
• accusative: суп

So:

• Я ем суп. = I am eating soup.
• Мне нужно доесть суп. = I need to finish the soup.

No visible ending change happens here.

It means finish the soup.

The verb доесть clearly implies that the soup has already been partly eaten and now needs to be eaten to the end.

Compare:

• есть суп = to eat soup
• съесть суп = to eat the soup, consume it
• доесть суп = to finish the remaining soup

So доесть is specifically about completing the action.

Both verbs here are perfective:

• дописать
• доесть

That makes sense because the speaker is talking about completing both actions.

Russian aspect here is important:

• писать = imperfective, process
• дописать = perfective, finish writing
• есть = imperfective, process
• доесть = perfective, finish eating

With нужно, both aspects are possible depending on meaning:

• Мне нужно писать отчёт весь вечер. = I need to write the report all evening.
  Focus on process.
• Мне нужно дописать отчёт до обеда. = I need to finish the report before lunch.
  Focus on completion.

So in your sentence, the perfective verbs show that the result matters.

Yes. Russian word order is flexible, though the original sentence is very natural.

Original:

• Мне нужно дописать отчёт до обеда, а потом доесть суп.

You could also hear:

• До обеда мне нужно дописать отчёт, а потом доесть суп.
• Мне нужно до обеда дописать отчёт, а потом доесть суп.

These all mean roughly the same thing, but the emphasis changes a little.

• До обеда at the beginning emphasizes the deadline
• Мне нужно early in the sentence emphasizes the speaker’s obligation
• the original order sounds neutral and smooth

In most modern standard Russian, обед usually corresponds to lunch, especially in a sentence like до обеда.

So:

• до обеда = before lunch / by lunchtime

However, depending on region, family habits, or older usage, meal terms can vary a bit. But for learners, lunch is the safest and most natural translation here.

Yes, slightly—and that may be part of its charm.

The sentence puts two very different unfinished things side by side:

• an unfinished report
• an unfinished bowl of soup

Russian allows this very naturally because the same до- idea works with both actions:

• дописать = finish writing
• доесть = finish eating

So grammatically it is perfectly normal, but stylistically it can sound a bit amusing because the speaker is treating office work and lunch in parallel.