Сімейний лікар чекає на пацієнта.

It means family doctor or general practitioner.

• сімейний = family
• лікар = doctor

Together, сімейний лікар is a fixed, very natural expression for the doctor who provides general primary care.

Because сімейний is an adjective agreeing with лікар.

In Ukrainian, adjectives must match the noun in:

• gender
• number
• case

Here, лікар is:

• masculine
• singular
• nominative

So the adjective must also be masculine singular nominative: сімейний.

Yes, лікар is grammatically masculine.

It can refer to a doctor in general, and in some contexts it may refer to a woman, especially in more traditional or official usage. But modern Ukrainian also very commonly uses the feminine form лікарка for a female doctor.

So:

• сімейний лікар = male family doctor, or sometimes doctor in a general sense
• сімейна лікарка = female family doctor

In your sentence, the grammar is masculine because the noun is лікар.

Чекає is the 3rd person singular present tense form of чекати (to wait).

So:

• я чекаю = I wait / I am waiting
• ти чекаєш = you wait
• він / вона чекає = he / she waits

Since сімейний лікар is a single person, the verb is singular: чекає.

Because Ukrainian usually does not need a subject pronoun when the subject is already stated or clear from context.

Here the subject is explicitly сімейний лікар, so adding він would be unnecessary.

English:

• The family doctor is waiting for the patient.

Ukrainian:

• Сімейний лікар чекає на пацієнта.

That is completely natural.

It can mean either, depending on context.

Ukrainian present tense often covers both:

• simple present: waits
• present continuous: is waiting

So чекає can mean:

• waits
• is waiting

In many real situations, English would naturally translate it as is waiting.

Here на is part of a common way to say wait for.

So:

• чекати на когось / на щось = to wait for someone / something

In this sentence:

• на пацієнта = for the patient

This construction is very natural in Ukrainian. You may also encounter чекати without на, but in this sentence the version with на is the one being used.

Because after на in this sentence, the noun is in the accusative case.

The dictionary form is:

• пацієнт = patient

But here we need the accusative singular:

• пацієнта

Since пацієнт is a masculine animate noun, its accusative singular looks like its genitive singular:

• nominative: пацієнт
• accusative: пацієнта

That is why the ending changes.

Ukrainian has no articles like English a or the.

So Ukrainian simply says:

• Сімейний лікар чекає на пацієнта.

Whether you translate that as:

• A family doctor is waiting for a patient
• The family doctor is waiting for the patient

depends on the context.

No, Ukrainian word order is more flexible than English word order because case endings show the grammatical roles.

The sentence as given:

• Сімейний лікар чекає на пацієнта.

is neutral and natural.

But other orders are possible, for example:

• На пацієнта чекає сімейний лікар.
  This puts more focus on the patient.
• Пацієнта чекає сімейний лікар.
  Also possible, with a different emphasis.

So the original order is the most straightforward, but it is not the only grammatical one.

A helpful stress guide is:

сіме́йний лі́кар чека́є на паціє́нта

Very roughly for an English speaker:

• сіме́йний ≈ see-MEY-nyy
• лі́кар ≈ LEE-kar
• чека́є ≈ che-KA-ye
• паціє́нта ≈ pa-tsi-YEN-ta

The exact sounds are not identical to English, but those approximations can help you get started.