Після того як аналіз крові підтвердив діагноз, лікар призначив лікування.

Yes. Після того як is a common way to say after when it introduces a whole clause.

• після = after
• того = that / of that
• як = how / as / when, depending on context

Together, після того як means after + a full action, like:

• Після того як він прийшов... = After he arrived...

This is different from using після with just a noun:

• після аналізу = after the test
• після того як аналіз підтвердив... = after the test confirmed...

So here it introduces the clause аналіз крові підтвердив діагноз.

You normally do not say Після як in standard Ukrainian.

The usual full pattern is:

• після того як = after

In everyday speech, Ukrainians may sometimes simplify other structures, but for a learner, після того як is the correct expression to use before a clause.

So:

• Після того як аналіз крові підтвердив діагноз... = correct
• Після як аналіз крові підтвердив діагноз... = not standard

Because крові is the genitive singular form of кров.

The noun аналіз often takes another noun in the genitive to show what kind of analysis/test it is:

• аналіз крові = blood test / analysis of blood
• аналіз сечі = urine test
• аналіз даних = analysis of data

So literally, аналіз крові means analysis of blood.

A useful pattern:

• X + genitive noun often means X of Y

It is genitive because it depends on аналіз.

In Ukrainian, when one noun describes another in an of relationship, the second noun is often put in the genitive:

• діагноз хвороби = diagnosis of the illness
• результат тесту = result of the test
• аналіз крові = analysis of blood

English often uses noun + noun combinations like blood test, but Ukrainian more often uses a noun plus the genitive case.

Because діагноз is the direct object of the verb підтвердив (confirmed), so it is in the accusative case.

For many masculine inanimate nouns, the accusative singular looks exactly like the nominative singular:

• nominative: діагноз
• accusative: діагноз

So in this sentence:

• аналіз крові підтвердив діагноз
• the blood test confirmed the diagnosis

Since діагноз is inanimate, its accusative form is the same as the basic dictionary form.

Because лікування is also the direct object, this time of призначив (prescribed).

The verb призначити usually takes a direct object in the accusative:

• призначити лікування = to prescribe treatment
• призначити ліки = to prescribe medicine
• призначити обстеження = to order an examination

Here, лікування is a neuter noun, and its accusative singular looks the same as its nominative singular:

• nominative: лікування
• accusative: лікування

Because the sentence describes two completed actions in the past:

1. the blood test confirmed the diagnosis
2. then the doctor prescribed treatment

Both verbs are masculine singular past forms:

• підтвердив = confirmed
• призначив = prescribed

They are masculine because their subjects are masculine nouns:

• аналіз is masculine
• лікар is masculine

If the subject were feminine, the past tense would change:

• лікарка призначила лікування = the female doctor prescribed treatment

They are perfective because the sentence refers to completed results:

• the test did confirm the diagnosis
• the doctor did prescribe treatment

In Ukrainian, perfective verbs are very common when you want to show that an action was completed successfully or reached its endpoint.

Here:

• підтверджувати = to be confirming / to confirm repeatedly or generally (imperfective)

• підтвердити = to confirm successfully, to establish (perfective)

• призначати = to prescribe / be prescribing (imperfective)
• призначити = to prescribe as a completed act (perfective)

The past tense forms used here are from the perfective verbs:

• підтвердив
• призначив

That fits the meaning very well: first the diagnosis was confirmed, then treatment was prescribed.

Because the sentence begins with a subordinate clause:

• Після того як аналіз крові підтвердив діагноз = subordinate time clause
• лікар призначив лікування = main clause

In Ukrainian, when a subordinate clause comes before the main clause, it is normally separated by a comma.

So the structure is:

• [After the blood test confirmed the diagnosis], [the doctor prescribed treatment].

This is very similar to English punctuation.

Yes. Ukrainian word order is more flexible than English word order, although not completely free.

The given sentence is neutral and natural:

• Після того як аналіз крові підтвердив діагноз, лікар призначив лікування.

You could also say:

• Лікар призначив лікування після того, як аналіз крові підтвердив діагноз.

This means the same thing, but the focus is slightly different. Starting with Після того як... emphasizes the time sequence first. Starting with Лікар призначив лікування... puts the doctor's action first.

Both are correct.

Because Ukrainian has no articles like English a/an/the.

So:

• лікар can mean a doctor or the doctor
• діагноз can mean a diagnosis or the diagnosis
• лікування can mean treatment or the treatment

You understand which one is meant from the context.

In this sentence, English naturally uses the because the context makes the diagnosis and the doctor specific. Ukrainian does not need a separate word for that.

Usually yes in this kind of sentence, although literally it means analysis of blood.

Depending on context, аналіз крові can be translated as:

• blood test
• blood analysis
• blood work (more conversational English, depending on context)

In a medical sentence like this, blood test is the most natural translation.

Stress is not shown in normal Ukrainian spelling, so unfortunately you usually have to learn it separately. For these words, the common stresses are:

• пІсля
• тогО
• як
• аналІз
• кровІ
• підтвердИв
• діагнОз
• лікАр
• призначИв
• лікувАння

Stress matters for pronunciation, and sometimes for understanding, so it is worth learning words together with their stress if you can.