W środę mam wizytę u lekarza o dziewiątej.

Because after w in this time expression, środa changes form.

• Dictionary form: środa = Wednesday
• In the sentence: w środę = on Wednesday

This is a very common pattern with days of the week in Polish. For Wednesday, the accusative form is środę.

So:

• środa = Wednesday
• w środę = on Wednesday

By itself, w środę simply means on Wednesday. The exact reference depends on context.

Depending on the situation, it could mean:

• this Wednesday
• next Wednesday
• just Wednesday in a general sense

If Polish speakers need to be more specific, they can add words such as:

• w tę środę = this Wednesday
• w przyszłą środę = next Wednesday

So w środę mam wizytę... is natural and normal, but context tells you which Wednesday is meant.

That is just the normal Polish way to express I have an appointment.

• mam = I have
• wizytę = a visit / appointment

So mam wizytę u lekarza literally looks like I have a visit at the doctor's, but in natural English it is simply I have a doctor's appointment.

This is a good example of how Polish and English package the same idea differently.

Because wizytę is the accusative form of wizyta.

• wizyta = nominative, the basic dictionary form
• wizytę = accusative

In mam wizytę, the noun is the direct object of mam (I have), so Polish uses the accusative.

Compare:

• To jest wizyta. = This is an appointment.
• Mam wizytę. = I have an appointment.

In this sentence, u means something like at or with, especially when talking about being at someone's place or with a professional.

So:

• u lekarza = at the doctor's / with the doctor

This is very common in Polish:

• u dentysty = at the dentist's
• u fryzjera = at the hairdresser's
• u znajomych = at some friends' place

So mam wizytę u lekarza is the normal way to say I have an appointment with the doctor.

Because the preposition u requires the genitive case.

• lekarz = doctor
• lekarza = of the doctor / doctor (genitive form)

So:

• u lekarza = at the doctor's / with the doctor

This is something worth memorizing as a set:

• u + genitive

For example:

• u nauczyciela = at the teacher's
• u kolegi = at a friend's place
• u lekarza = at the doctor's

Not in this sentence.

• mam wizytę u lekarza = I have an appointment with the doctor
• idę do lekarza = I’m going to the doctor

So the difference is:

• u lekarza describes the appointment/location/relationship with the doctor
• do lekarza emphasizes movement toward the doctor

If you say Mam wizytę do lekarza, that is not correct Polish.

A natural pair is:

• W środę mam wizytę u lekarza.
• W środę idę do lekarza.

Both can be translated naturally, but they are built differently.

Because Polish normally tells the exact hour with an ordinal form, not the plain number.

So:

• dziewięć = nine
• dziewiąta = ninth
• o dziewiątej = at nine o'clock

This comes from an understood phrase like o dziewiątej godzinie = at the ninth hour, where godzinie is usually omitted.

That is why the form is dziewiątej, not dziewięć.

More examples:

• o pierwszej = at one
• o piątej = at five
• o jedenastej = at eleven

It is in the locative, because the preposition o in this time expression takes the locative.

The full underlying idea is something like:

• o dziewiątej godzinie = at the ninth hour

Since godzina is feminine, the ordinal also appears in a feminine form:

• pierwszej
• drugiej
• trzeciej
• dziewiątej

In everyday speech, Polish drops godzinie, but the form of the ordinal stays the same.

By itself, it can mean either. Context decides.

In a sentence about a doctor's appointment, most people will probably assume 9 a.m., but grammatically it is not stated.

If you want to make it explicit, you can say:

• o dziewiątej rano = at 9 in the morning
• o dziewiątej wieczorem = at 9 in the evening

So o dziewiątej alone just means at nine o'clock.

No, Polish word order is fairly flexible.

This sentence starts with W środę to foreground the day. But you could also say:

• Mam wizytę u lekarza w środę o dziewiątej.
• O dziewiątej mam wizytę u lekarza w środę.

These versions all mean basically the same thing, but the emphasis changes.

The given sentence sounds very natural. It puts the day first, then the main information, then the exact time.

Because Polish usually drops subject pronouns when the verb already shows who the subject is.

• mam already means I have

So:

• mam = I have
• ja mam = I have, with extra emphasis or contrast

You would use ja only if you want to stress it, for example:

• Ja mam wizytę u lekarza, a on nie.
  I have a doctor's appointment, but he doesn't.

In a neutral sentence, leaving out ja is normal.

Because Polish has no articles.

So wizytę can mean:

• an appointment
• the appointment

and u lekarza can mean:

• with a doctor
• with the doctor

Context tells you which meaning is intended.

That is why mam wizytę u lekarza can be translated naturally as I have a doctor's appointment without any separate Polish word for a or the.