Налоговый вычет выбрали исходя из расходов на лечение.

It actually is the direct object, but in this sentence the form looks the same as the nominative.

• выбрать takes the accusative case.
• вычет is an inanimate masculine noun.
• For inanimate masculine singular nouns, the accusative = nominative.

So:

• nominative: налоговый вычет
• accusative: налоговый вычет

That is why the object does not change its form here.

Russian often uses a 3rd person plural past tense with no stated subject to mean they chose, someone chose, or it was chosen in an impersonal/indefinite way.

So выбрали does not necessarily mean a specific they. In official or bureaucratic language, it often works a lot like an English passive:

• Налоговый вычет выбрали... = The tax deduction was chosen... / They chose the tax deduction...

This is very common in Russian.

Because выбрали is perfective, and it presents the action as completed.

• выбрали = they chose / they have chosen
• выбирали = they were choosing / they used to choose / they chose repeatedly or with focus on process

In this sentence, the result matters: a deduction was selected, so perfective выбрали is the natural choice.

Исходя из is a very common expression meaning:

• based on
• proceeding from
• taking into account
• on the basis of

So the sentence says that the deduction was chosen based on the treatment expenses.

Although исходя originally comes from a verb, исходя из is very often learned and used as a fixed expression.

It takes the genitive case.

That is why you get:

• из расходов
• not из расходы

This is similar to many other uses of из, which also require the genitive.

Because расходов is the genitive plural form of расходы.

Here that happens for two reasons:

1. исходя из requires the genitive.
2. расходы is naturally plural in the meaning expenses/costs.

So:

• nominative plural: расходы
• genitive plural: расходов

Because Russian commonly says расходы на что? = expenses for/on what?

So:

• расходы на лечение = expenses for treatment
• расходы на обучение = expenses for education
• расходы на ремонт = expenses for repairs

The preposition на here takes the accusative.

It is in the accusative, but the accusative form is identical to the nominative for this noun.

Лечение is a neuter inanimate noun, so:

• nominative: лечение
• accusative: лечение

That is why you do not see a visible ending change.

Yes, historically исходя is an adverbial participle (often called a verbal adverb or gerund-like form), from исходить.

However, in modern Russian исходя из is very often treated almost like a fixed prepositional expression meaning based on. In formal and bureaucratic language, it is commonly written without a comma when it is closely tied to the predicate.

So in a sentence like this, no comma is normal.

Yes. Russian word order is flexible, and the meaning would stay similar, though the emphasis changes.

For example:

• Налоговый вычет выбрали исходя из расходов на лечение.
• Выбрали налоговый вычет исходя из расходов на лечение.

The original version puts налоговый вычет first as the topic: as for the tax deduction, it was chosen...

That kind of word order is especially common in formal written Russian.

Yes. Because Russian uses an indefinite выбрали with no subject, English can often translate it in more than one way.

Possible translations include:

• They chose the tax deduction based on treatment expenses.
• The tax deduction was chosen based on treatment expenses.
• The deduction was selected on the basis of treatment expenses.

In natural English, the passive is often best if the agent is unknown or unimportant.

In Russian, расходы is the normal word for expenses/costs in financial, legal, and bureaucratic language. Even when English might use a more abstract singular like expense or cost, Russian often prefers the plural.

So расходы на лечение is the standard collocation for medical/treatment expenses.