Банщик решил запарить банный веник.

Решил is the past tense, masculine singular form of решить (to decide).

It agrees with банщик, which is a masculine singular noun, so the verb is also masculine singular in the past:

• банщик решил = the bathhouse attendant decided
• if it were a woman: банщица решила
• plural: банщики решили

In Russian past tense, verbs change for gender in the singular:

• masculine: -л
• feminine: -ла
• neuter: -ло
• plural: -ли

So решил immediately tells you the subject is masculine singular.

After решить, Russian commonly uses an infinitive to say what someone decided to do.

So:

• решил запарить = decided to steam/soak
• literally: decided [to steam/soak]

This is a very common pattern:

• Я решил уйти. = I decided to leave.
• Она решила подождать. = She decided to wait.

So in your sentence, решил запарить works just like English decided to prepare/steam.

Here запарить means something like to steam, to soak in hot water, or to prepare by steaming, specifically in the context of a баня.

A банный веник is typically soaked or steamed before use, so запарить веник is a set phrase in bathhouse culture.

A useful thing to know is that запарить can have other meanings in other contexts, including colloquial ones, but here the bathhouse context makes the meaning clear:
to prepare the whisk by soaking/steaming it.

Запарить is a perfective verb. Perfective verbs usually present an action as a completed whole or a single result.

That fits this sentence well, because the idea is not just to be steaming the whisk in general, but to prepare it fully.

Compare the aspectual idea:

• парить / запаривать = imperfective, process/habit/repetition
• запарить = perfective, one completed action/result

So решил запарить sounds natural because it means he decided to carry out that preparation.

Банный is an adjective meaning bathhouse-related or for the bathhouse. It comes from баня (bathhouse, steam bath).

It is банный because it must agree with веник, which is:

• masculine
• singular
• here effectively in the accusative, but since it is inanimate, that looks the same as nominative

So the adjective also appears in the masculine singular form:

• банный веник

Other forms would appear with different nouns:

• банная шапка = a bathhouse hat/cap
• банное полотенце = a bathhouse towel
• банные принадлежности = bathhouse items

Literally, веник often means broom or bundle of twigs. But in баня culture, банный веник is a special object: a bundle of leafy branches used in the steam bath.

So in this sentence, it does not mean an ordinary floor broom. It refers to the traditional bath whisk used in a Russian bathhouse.

This is one of those words where the exact meaning depends heavily on context.

Because веник is a masculine inanimate noun.

In Russian, for masculine inanimate nouns, the accusative singular is usually the same as the nominative singular.

So:

• nominative: веник
• accusative: веник

That is why after the verb запарить you still see веник, not a different-looking form.

Compare with an animate noun:

• Я вижу стол. = I see a table.
  (стол is inanimate, so accusative = nominative)
• Я вижу брата. = I see my brother.
  (брат is animate, so accusative = genitive)

Both are possible in principle, but банный веник is the normal, compact, idiomatic way to say it.

Russian often prefers an adjective where English might use a noun modifier or a longer phrase:

• банный веник = literally bathhouse whisk
• веник для бани = a whisk for the bathhouse

The adjective form is more natural here because it is a common established collocation.

The standard stress is:

Ба́нщик реши́л запа́рить ба́нный ве́ник.

Word by word:

• ба́нщик
• реши́л
• запа́рить
• ба́нный
• ве́ник

A learner may especially want to notice:

• реши́л, not ре́шил
• запа́рить, stress on па
• ве́ник, stress on the first syllable

This is a very normal, neutral word order:

Банщик решил запарить банный веник.

It follows a straightforward pattern:

• subject: банщик
• verb: решил
• infinitive: запарить
• object: банный веник

Russian word order is flexible, so other orders are possible, but they would change the emphasis:

• Банный веник банщик решил запарить.
  Emphasizes the bath whisk
• Запарить банный веник банщик решил.
  Sounds marked or literary, with focus on the action

For a textbook-style neutral sentence, the given order is the most natural.

Yes: the sentence makes much more sense if you know a little about the Russian баня.

A банный веник is a traditional bundle of branches used in the steam bath. Before using it, people often soak or steam it in hot water to soften the leaves and release aroma. That is exactly why the verb запарить is used here.

So even though the grammar is straightforward, the phrase reflects a very specific cultural practice.

Yes. Банщик is the person associated with work in the баня, and depending on context it may suggest:

• a bathhouse attendant
• a bathhouse worker
• someone who helps prepare or conduct bath procedures

In cultural or literary contexts, it can evoke a fairly specific traditional role, not just any employee in a building. So банщик is more specific than simply worker.

Yes, but it would change the nuance.

For example, запаривать would be the imperfective counterpart. It could suggest:

• process
• repetition
• habit
• a less bounded action

But with решил, Russian often prefers a perfective infinitive when the speaker means decided to do and complete a specific action.

So:

• решил запарить = decided to steam/prepare it fully
• решил запаривать = would sound less natural in this context unless you mean something more like decided to start steaming it regularly / decided to be engaged in the process

That is why запарить is the natural choice here.