Muszę jeszcze pomyśleć o nowym planie.

Muszę means I must or I have to.

In Polish, the verb ending usually already shows who the subject is, so ja (I) is often omitted.

• muszę = I must / I have to
• musisz = you must
• musi = he/she/it must

So Muszę jeszcze pomyśleć... already clearly means I still need to think...

You can add ja for emphasis, for example if you want to contrast yourself with someone else:

• Ja muszę jeszcze pomyśleć. = I still need to think.

Without emphasis, leaving out the pronoun is the normal choice.

After muszę (I have to / I must), Polish normally uses an infinitive, just like English often does:

• Muszę iść. = I have to go.
• Muszę pracować. = I have to work.
• Muszę pomyśleć. = I have to think.

So in this sentence:

• Muszę = I have to
• pomyśleć = to think

Together: Muszę pomyśleć = I need to think

This is about aspect, which is very important in Polish verbs.

• myśleć = imperfective
• pomyśleć = perfective

Very roughly:

• myśleć focuses on the process: to be thinking / to think in general
• pomyśleć often means to think something over, to give something some thought, or to think for a moment and reach some result

In Muszę jeszcze pomyśleć o nowym planie, the speaker means something like:

• I still need to think it over
• I need to give some more thought to the new plan

So pomyśleć sounds natural because it presents the thinking as a bounded action that still needs to happen.

In this sentence, jeszcze means still, yet, or a bit more, depending on context.

So:

• Muszę pomyśleć = I need to think
• Muszę jeszcze pomyśleć = I still need to think / I need to think a bit more

It suggests that the speaker is not ready yet and needs more time to consider the matter.

In other contexts, jeszcze can also mean more or another, so it is a very flexible word.

The preposition o often means about when talking about thinking, speaking, reading, writing, etc.

So:

• myśleć o czymś = to think about something
• mówić o czymś = to talk about something

In your sentence:

• o nowym planie = about the new plan

This is simply the standard preposition used with myśleć / pomyśleć in this meaning.

Because the preposition o requires the locative case in this usage.

The basic form is:

• plan = plan

But after o, it changes to the locative:

• o planie = about the plan

So:

• myśleć o planie = to think about the plan

This is a very common pattern in Polish:

• o domu = about the house
• o pracy = about work
• o człowieku = about the person

Because adjectives have to match the noun in case, gender, and number.

The noun plan is masculine singular.
After o, it becomes locative singular:

• plan → planie

The adjective nowy also has to change into the locative singular masculine form:

• nowy → nowym

So:

• nowy plan = a new plan
• o nowym planie = about a new plan

Both words change together:

• adjective: nowy → nowym
• noun: plan → planie

Polish does not have articles like a and the, so o nowym planie can mean either:

• about a new plan
• about the new plan

The exact meaning depends on context.

If the plan has already been mentioned, English will often use the:

• I still need to think about the new plan.

If it is being introduced for the first time, English may use a:

• I still need to think about a new plan.

Polish leaves that distinction unstated unless the context makes it clear.

Yes, Polish word order is more flexible than English, although some orders sound more neutral than others.

The neutral version here is:

• Muszę jeszcze pomyśleć o nowym planie.

You might also hear:

• Jeszcze muszę pomyśleć o nowym planie.
• O nowym planie muszę jeszcze pomyśleć.

These versions shift emphasis a little:

• starting with jeszcze emphasizes still / yet
• starting with o nowym planie emphasizes about the new plan

But the original sentence is the most straightforward and natural in many contexts.

Yes, but the nuance is a little different.

• myśleć o czymś = to think about something
• myśleć nad czymś = to think something over, to work mentally on something, often with a stronger sense of active consideration

So:

• Muszę jeszcze pomyśleć o nowym planie.
  = I still need to think about the new plan.

• Muszę jeszcze pomyśleć nad nowym planem.
  = I still need to think over / work on the new plan.

Both can be correct, but o nowym planie is the more basic and direct equivalent of about the new plan.

These words can be tricky for English speakers.

A rough guide:

• muszę ≈ MOO-sheh
• jeszcze ≈ YESH-cheh
• pomyśleć ≈ po-MISH-lech or po-MISH-letch as a rough approximation

A few important sound notes:

• sz sounds like English sh
• cz sounds like English ch
• ś is a softer sound than sh
• ę is a nasal vowel, but at the end of a word like muszę, in normal speech it is often pronounced close to e or eh with slight nasal coloring

So even if the spelling looks intimidating, the sentence becomes much easier once you recognize those common Polish letter combinations.