Jeśli odpocznę po obiedzie, dam radę przygotować prezentację na jutro.

In Polish, perfective verbs do not have a normal present tense. Their present-looking forms are used to express the future.

So here:

• odpocznę = I will rest
• dam = I will give / I will manage in this expression

The base verbs here are perfective:

• odpocząć = to rest up, to have a rest (perfective)
• dać = to give (perfective)

That is why Polish does not say będę odpocząć or będę dać.

Compare:

• odpoczywam = I am resting / I rest (imperfective present)
• odpocznę = I will rest (perfective future)

Because the sentence refers to one completed action in the future: if I rest after lunch. Polish often uses a perfective verb for that idea.

• odpocznę suggests a single, completed act of resting
• będę odpoczywać would mean I will be resting, focusing more on the ongoing process

In this sentence, the speaker means:

• first I rest,
• then I will be able to prepare the presentation

So odpocznę fits better.

Dać radę is a very common Polish expression meaning:

• to manage
• to cope
• to be able to do something
• to succeed in doing something

So:

• dam radę przygotować prezentację = I’ll manage to prepare the presentation
• nie dam rady = I won’t manage / I won’t be able to do it

It is partly idiomatic, so it is best learned as a set phrase:

• dać radę + infinitive

Examples:

• Dam radę to zrobić. = I’ll manage to do it.
• Nie dam rady przyjść. = I won’t be able to come.

Because rada changes form here. In the expression dać radę, the noun appears in the accusative case:

• nominative: rada
• accusative: radę

So the fixed expression is:

• dać radę

not

• dać rada

Even though the whole phrase is idiomatic, grammatically it still follows normal case rules.

After the preposition po in this meaning (after), Polish uses the locative case.

So:

• obiad = lunch / dinner
• po obiedzie = after lunch / after dinner

This is why obiad changes to obiedzie.

A few similar examples:

• po pracy = after work
• po szkole = after school
• po filmie = after the film

It can depend on context and culture.

In Polish, obiad is usually the main meal of the day, often eaten in the afternoon. In English, that might be translated as:

• lunch
• dinner

In your sentence, po obiedzie is often best translated as after lunch, but after dinner could also be possible depending on the situation.

Because prezentacja is the direct object of the verb przygotować (to prepare), and direct objects often take the accusative case in Polish.

So:

• nominative: prezentacja
• accusative: prezentację

That gives:

• przygotować prezentację = to prepare a presentation

This is a very normal pattern:

• czytać książkę = to read a book
• pisać wiadomość = to write a message
• robić kawę = to make coffee

Na jutro means something like:

• for tomorrow
• by tomorrow

So:

• przygotować prezentację na jutro = prepare the presentation for tomorrow

This suggests the presentation is needed tomorrow.

By contrast:

• jutro simply means tomorrow

Compare:

• Przygotuję prezentację jutro. = I will prepare the presentation tomorrow.
• Przygotuję prezentację na jutro. = I will prepare the presentation for tomorrow.

So na jutro is about the deadline or occasion, not just the time of doing the action.

Because Polish usually leaves out subject pronouns when they are clear from the verb ending.

Here:

• odpocznę already means I will rest
• dam already means I will manage

So ja is unnecessary.

You could say:

• Jeśli ja odpocznę po obiedzie, dam radę...

but that would sound more emphatic, as if stressing I in contrast to someone else.

Yes. Polish word order is fairly flexible.

The original sentence:

• Jeśli odpocznę po obiedzie, dam radę przygotować prezentację na jutro.

You could also say:

• Dam radę przygotować prezentację na jutro, jeśli odpocznę po obiedzie.

Both are correct. The difference is mainly in focus and style.

The original version starts with the condition:

• If I rest after lunch...

The second version starts with the result:

• I’ll manage to prepare the presentation...

Because Polish normally uses a comma before or after a subordinate clause introduced by words like jeśli (if).

So in:

• Jeśli odpocznę po obiedzie, dam radę...

the clause Jeśli odpocznę po obiedzie is separated from the main clause by a comma.

This is standard Polish punctuation.

The infinitive is odpocząć.

This can look confusing because the stem changes:

• odpocząć = infinitive
• odpocznę = I will rest
• odpoczniesz = you will rest

This kind of consonant change is normal in Polish verb conjugation and is something learners often just have to get used to.

Also note the aspect pair:

• odpoczywać = to be resting / to rest habitually (imperfective)
• odpocząć = to rest up, to have a rest once/completely (perfective)

Sometimes, but the meaning shifts slightly.

• dam radę = I’ll manage / I’ll be able to do it successfully
• będę mógł = I will be able to
• mogę = I can / may

In this sentence, dam radę sounds natural because it suggests having enough energy or capacity to get it done.

Compare:

• Jeśli odpocznę po obiedzie, dam radę przygotować prezentację na jutro.
  = If I rest after lunch, I’ll manage to prepare the presentation for tomorrow.

• Jeśli odpocznę po obiedzie, będę mógł przygotować prezentację na jutro.
  = If I rest after lunch, I will be able to prepare the presentation for tomorrow.

The second is also possible, but dam radę feels a bit more like I’ll be up to it / I’ll cope.