Po drodze kupię chleb i mleko.

It means on the way or along the way.

So Po drodze kupię chleb i mleko means something like:

• I’ll buy bread and milk on the way
• I’ll pick up bread and milk on the way

It usually suggests that the speaker is going somewhere, and during that trip they will stop and buy these things.

Kupię is the future tense of kupić, which is a perfective verb.

• kupić = to buy in the sense of completing the purchase
• kupię = I will buy

By contrast, kupuję means I am buying or I buy.

So:

• kupuję chleb = I’m buying bread / I buy bread
• kupię chleb = I’ll buy bread

In this sentence, the speaker is talking about a future, completed action, so kupię is the natural choice.

This is a very common Polish aspect pair:

• kupić = perfective
• kupować = imperfective

Very roughly:

• perfective focuses on a completed result
• imperfective focuses on the process, repetition, or ongoing action

Examples:

• Kupię chleb. = I’ll buy bread.
  The purchase will be completed.
• Będę kupować chleb. = I’ll be buying bread.
  This sounds more like focusing on the activity itself, not just the result.
• Kupuję chleb codziennie. = I buy bread every day.

In your sentence, kupię fits because the speaker simply means they will get the bread and milk.

Because Polish often omits subject pronouns when the verb already makes the subject clear.

The ending -ę in kupię tells you the subject is I.

So:

• Kupię chleb i mleko. = I’ll buy bread and milk.
• Ja kupię chleb i mleko. also means I’ll buy bread and milk, but ja adds emphasis, like I will.

English usually needs the pronoun, but Polish often does not.

They are the direct objects of kupię, so they are in the accusative case. But for these particular nouns, the accusative looks the same as the nominative.

• chleb = nominative singular

• chleb = accusative singular

• mleko = nominative singular
• mleko = accusative singular

This is very common with inanimate masculine nouns like chleb and neuter nouns like mleko.

So even though the case is accusative, the forms do not visibly change here.

Drodze is the locative singular form of droga (road, way).

The preposition po often requires the locative case, so:

• droga → drodze

That consonant change may look strange at first, but it is normal in Polish declension.

So:

• po drodze literally relates to on the road / on the way
• as a whole, it is a fixed everyday expression meaning on the way

It is both.

You can analyze it grammatically:

• po = a preposition
• drodze = locative of droga

But in practice, po drodze is also a very common fixed expression meaning:

• on the way
• along the way

So learners often do best by memorizing po drodze as a chunk.

Not in the same sense as the English conversation marker by the way.

In this sentence, po drodze clearly means physically on the way somewhere.

If you want the conversational by the way, Polish more often uses expressions like:

• przy okazji
• a propos

So:

• Po drodze kupię chleb i mleko. = I’ll buy bread and milk on the way.
• It does not mean By the way, I’ll buy bread and milk.

Yes, usually there is.

Po drodze often implies on the way to some place that is already understood from context.

For example, the speaker might mean:

• on the way home
• on the way to work
• on the way to someone’s house

Polish does not need to state that destination if it is obvious from the situation.

So the sentence feels natural even without saying exactly on the way where.

Yes. Polish word order is relatively flexible, though the emphasis changes.

Your original sentence:

• Po drodze kupię chleb i mleko.

Other possible versions:

• Kupię po drodze chleb i mleko.
• Chleb i mleko kupię po drodze.

All of these can be correct, but they sound slightly different in emphasis.

The original version is very natural if you want to foreground on the way.

Usually as a simple, everyday promise or plan:

• I’ll pick up bread and milk on the way.

It sounds natural, practical, and conversational. A native speaker would probably imagine that the person is saying they do not need a special trip to the store because they can buy these things while already going somewhere else.

A careful approximation is:

po DRO-dze KOO-pye HLEP ee MLE-ko

A few helpful notes:

• po sounds roughly like po in pole, but shorter
• drodze has dz pronounced like the ds in beds
• kupię is roughly KOO-pye
• ch in chleb is like a rough h sound, not English ch
• mleko is roughly MLE-ko, with the ml cluster clearly pronounced

The stress in Polish usually falls on the second-to-last syllable:

• dRO-dze
• KU-pię
• MLE-ko

Yes, in natural English that is often a very good translation.

Literally, kupię means I will buy, but depending on context, English may prefer:

• I’ll buy bread and milk on the way
• I’ll get bread and milk on the way
• I’ll pick up bread and milk on the way

All of these can work. Get and pick up often sound especially natural in everyday English.