Po návštěvě zubařky půjdu do lékárny pro lék.

Po návštěvě means after the visit.

The preposition po can mean after, and when it is used in this time sense, it is followed by the locative case.

• dictionary form: návštěva = visit
• locative singular: návštěvě

So:

• po návštěvě = after the visit

This is a very common pattern in Czech:

• po práci = after work
• po obědě = after lunch
• po škole = after school

Because návštěva often takes the person visited in the genitive.

So:

• návštěva zubařky = a visit to the female dentist

Here the base noun is:

• zubařka = female dentist

Its genitive singular is:

• zubařky

A useful comparison:

• návštěva lékaře = a visit to the doctor
• návštěva kamaráda = a visit to a friend
• návštěva zubařky = a visit to the female dentist

So the structure is basically visit of/to someone, where Czech uses the genitive.

Yes. Zubařka specifically means a female dentist.

Compare:

• zubař = dentist, usually male or sometimes generic in casual use
• zubařka = female dentist

So this sentence tells you the dentist is female.

A learner may expect something more neutral, but Czech often marks gender directly in professions.

Půjdu is the future tense of jít (to go on foot / to go).

• jdu = I am going / I go
• půjdu = I will go

Since the sentence talks about what will happen after the dentist visit, the future is natural:

• Po návštěvě zubařky půjdu... = After visiting the dentist, I’ll go...

In spoken Czech, jdu can sometimes refer to the near future, but půjdu is clearer and more standard here.

Because do is used for movement to/into an enclosed place or destination, and it takes the genitive.

• lékárna = pharmacy
• do lékárny = to the pharmacy

Compare:

• jdu do školy = I’m going to school
• jdu do obchodu = I’m going to the shop
• jdu do lékárny = I’m going to the pharmacy

If you were talking about being inside the pharmacy, you would use:

• v lékárně = in the pharmacy

So:

• do lékárny = movement toward it
• v lékárně = location inside it

Pro lék means to get medicine or for medicine in the sense of to pick it up.

In Czech, the pattern jít pro něco means:

• to go get something
• to go pick something up

So:

• jdu pro chléb = I’m going to get bread
• jdu pro děti = I’m going to pick up the children
• jdu pro lék = I’m going to get medicine

The preposition pro takes the accusative case.

Here:

• lék is masculine inanimate
• accusative singular = lék (same form as nominative)

So pro lék is grammatically exactly what you would expect after pro.

Yes, in this sentence lék means medicine, a drug, or a remedy.

A few useful nuances:

• lék = a medicine / remedy / drug
• léky = medicines
• medicína usually means medicine as a field of study, not a pill or drug

In this context, lék probably means some medicine the speaker needs after the dentist appointment, possibly prescribed medicine.

So do lékárny pro lék is a very natural phrase.

Because Czech has no articles.

English says:

• the dentist
• a pharmacy
• the medicine

Czech usually just says:

• zubařka
• lékárna
• lék

Whether something is the, a, or just a general idea is understood from context.

So in this sentence, English needs articles, but Czech does not.

Yes. Czech word order is relatively flexible, because the cases show the grammatical roles.

The given sentence:

• Po návštěvě zubařky půjdu do lékárny pro lék.

is a natural neutral order. It starts with the time expression after visiting the dentist, then gives the main action.

You could also say things like:

• Půjdu po návštěvě zubařky do lékárny pro lék.
• Do lékárny půjdu po návštěvě zubařky pro lék.

These are all possible, but the emphasis changes slightly.

The original version is good because it clearly sets up the sequence of events first.

Yes, that is also possible, and many learners find it easier to understand.

Compare:

• po návštěvě zubařky
• po návštěvě u zubařky

Both can mean after a visit to the female dentist.

The version without u is compact and very natural. The version with u may feel more transparent to a learner because u zubařky clearly means at the dentist’s place / at the female dentist.

So the original sentence is correct, but po návštěvě u zubařky is also a useful alternative to know.

Yes. It describes a sequence of future events:

1. the dentist visit happens
2. after that, the speaker will go to the pharmacy
3. the purpose is to get medicine

So the sentence is not just about movement. It also expresses time order and purpose:

• Po návštěvě zubařky = after the dentist visit
• půjdu do lékárny = I’ll go to the pharmacy
• pro lék = to get medicine

That makes it a very useful model sentence, because it combines several common Czech structures in one line.