Nie dam dziś rady skończyć całego raportu.

It is a very common Polish expression meaning I won’t manage, I won’t be able to, or I can’t handle it in a practical sense.

So in this sentence, nie dam rady is not about literally giving advice or giving a council. It is an idiom:

• dać radę = to manage, to cope, to succeed in doing something
• nie dać rady = not to manage, not to be able to do something

It often sounds a bit more everyday and practical than a more literal ability phrase like nie będę mógł.

Because Polish usually does not need subject pronouns when the verb already shows who the subject is.

Here, dam already tells you it is 1st person singular: I will manage / I will give.

So:

• dam = I will
• nie dam = I won’t

You could say Ja nie dam dziś rady..., but adding ja would usually give extra emphasis, like I won’t manage.

This is one of the most important things to notice: dać is a perfective verb.

In Polish, perfective verbs do not normally have a true present meaning. Their present-looking forms usually refer to the future.

So:

• dam literally looks like a present form
• but it means I will give / I will manage

That is why Nie dam dziś rady means I won’t manage today, not I don’t manage today.

Because dać radę is a fixed expression, and in that expression the noun appears as radę / rady, not plain rada.

In this idiom:

• dać radę = to manage
• nie dać rady = not to manage

Here you are seeing rady, which is part of that established pattern. For a learner, the best approach is to memorize dać radę as a whole expression rather than trying to interpret it word by word.

Even though rada by itself can mean advice or counsel, that is not the literal meaning here.

Because after dać radę, Polish normally uses an infinitive to say what someone manages or does not manage to do.

So the structure is:

• dać radę + infinitive
• nie dać rady + infinitive

Here:

• nie dam rady = I won’t manage
• skończyć = to finish

Together: I won’t manage to finish...

This is similar to English to manage to do something.

Because skończyć is the perfective verb, and it means to finish completely.

Compare:

• kończyć = to be finishing / to finish in a general or ongoing sense
• skończyć = to finish, to bring to completion

Since the sentence is about completing the report, skończyć is the natural choice.

So:

• skończyć raport = finish the report
• kończyć raport would sound more like be finishing the report or refer to the process rather than the completed result

This is about case, and specifically about genitive under negation.

Normally, with a positive verb, you would expect the direct object in the accusative:

• skończyć cały raport = to finish the whole report

But in negative contexts, Polish often changes the object to the genitive:

• całego raportu

That is very common after negated expressions of ability such as:

• nie mogę
• nie umiem
• nie dam rady

So in this sentence, całego raportu is a very natural and standard choice.

Also notice agreement:

• cały raport = accusative / nominative-type form
• całego raportu = genitive form

Both the adjective and the noun change.

It means the whole or the entire.

So:

• skończyć raport = finish the report
• skończyć cały raport = finish the whole report
• nie dam rady skończyć całego raportu = I won’t manage to finish the entire report

It emphasizes that the speaker is talking about completing all of it, not just part of it.

Yes. Both mean today.

• dziś = today
• dzisiaj = today

The difference is mostly stylistic:

• dziś is shorter
• dzisiaj is a bit fuller

Both are very common and natural in everyday Polish.

Yes. Polish word order is fairly flexible, and changing it often changes emphasis rather than basic meaning.

Your sentence:

• Nie dam dziś rady skończyć całego raportu.

Other natural possibilities:

• Dziś nie dam rady skończyć całego raportu.
• Nie dam rady dziś skończyć całego raportu.

The meaning stays very similar, but the focus shifts slightly:

• Dziś at the beginning puts extra emphasis on today
• the original version sounds very natural and neutral

They are close in meaning, but the nuance is slightly different.

• nie dam rady often sounds more practical and everyday
  • I won’t manage
  • I don’t have enough time/energy/capacity
• nie będę mógł is more neutral and literal
  • I will not be able to

So:

• Nie dam dziś rady skończyć całego raportu feels like I won’t manage to finish the whole report today
• Nie będę mógł skończyć dziś całego raportu is more like I won’t be able to finish the whole report today

Both are correct, but nie dam rady is very common in spoken Polish.

Yes. It can stand on its own.

• Nie dam dziś rady. = I won’t manage today.

That already makes sense. The infinitive phrase skończyć całego raportu simply tells you what the speaker won’t manage to do.

So the full sentence is just a more specific version of a complete statement.

Yes, in many contexts it would be possible.

• skończyć = finish
• dokończyć = finish off, finish something that has already been started

Since a report is usually something you are already working on, dokończyć cały raport could also sound natural. But skończyć cały raport is perfectly normal and broad.

So:

• skończyć = neutral finish
• dokończyć = more explicitly complete what is already underway