bouringuzyou de, bouringusyuuzu, pin, sukoaboodo, booruritaan wo kakuninsuru.

で marks the place where an action happens.

So in ボウリング場で, the meaning is at the bowling alley or in the bowling alley as the location where the checking takes place.

A useful comparison:

• に often marks existence or destination
• で marks the location of an action

Here, 確認する is an action, so で is the natural choice.

Because the entire list is treated as one object of 確認する.

So:

• ボウリングシューズ、ピン、スコアボード、ボールリターンを確認する

means:

• check the bowling shoes, pins, scoreboard, and ball return

Japanese often puts を only once after the final item in a list, instead of after every noun.

Japanese can list nouns in more than one way.

Here, commas are being used to present a simple list:

• ボウリングシューズ、ピン、スコアボード、ボールリターン

This is common in checklists, instructions, captions, and educational materials.

If you used と, it would sound more like a clearly connected list:

• ボウリングシューズとピンとスコアボードとボールリターンを確認する

That is grammatical, but less natural for this kind of checklist-style sentence.

確認する means to check, to confirm, or to make sure of something.

It often has the nuance of verifying that something is present, correct, or in the expected condition.

So here it does not just mean look at. It suggests something more like:

• check that these things are there
• make sure they are correct
• verify them

In an instructional context, 確認する is very common.

The dictionary form is often used in:

• headings
• instructions
• manuals
• captions
• checklist items
• descriptions of actions

So this sentence sounds like an instruction or label, not a full polite spoken sentence.

For example:

• ボウリング場で、ボウリングシューズ、ピン、スコアボード、ボールリターンを確認する。

has a neutral, textbook/checklist feel.

A polite spoken version would be:

• ボウリング場で、ボウリングシューズ、ピン、スコアボード、ボールリターンを確認します。

Yes. Japanese often leaves out the subject when it is understood from context.

Depending on the situation, the implied subject could be:

• you — in instructions
• we — in a group activity
• I — in a self-description
• a general subject like one

In this sentence, because it sounds instructional, the implied subject is probably something like you:

• At the bowling alley, check the bowling shoes, pins, scoreboard, and ball return.

Mostly yes.

These are loanwords or foreign-style terms commonly written in katakana:

• ボウリング場 — bowling alley
  
  • ボウリング is from English bowling
  • 場 is a native/Japanese-origin kanji meaning place
• ボウリングシューズ — bowling shoes
• スコアボード — scoreboard
• ボールリターン — ball return

ピン is also a loanword and in this context means bowling pins.

Katakana is the normal script for these kinds of words.

It means the ball return—the machine or mechanism that sends the bowling ball back after it is rolled.

This is one of those expressions that may sound slightly specialized in English, but in Japanese it is a normal katakana term in a bowling context.

So it refers to the place/device where the ball comes back to the players.

場 means place, site, or venue.

So:

• ボウリング場 literally means
• bowling place

In natural English, that becomes bowling alley or bowling center.

The reading here is じょう, so:

• ボウリング場 = ボウリングじょう

This pattern appears in many words:

• 工場 = factory
• 会場 = venue
• 駐車場 = parking lot

Yes, because of the context.

ピン can mean different kinds of pin depending on context, but in a bowling-related sentence, it naturally means bowling pins.

Since the sentence is about things to check at a bowling alley, there is no real ambiguity.

You are right: normal Japanese writing usually does not use spaces between words.

This sentence has spaces most likely because it comes from:

• teaching material
• a worksheet
• a reading aid
• a layout designed to make parts easier to see

A more normally written version would be:

• ボウリング場で、ボウリングシューズ、ピン、スコアボード、ボールリターンを確認する。

So the spaces are not part of standard grammar; they are just formatting.

Yes, depending on context.

Even though 確認する is dictionary form, in instructions it can function like a command or task description.

So it may be understood as:

• Check the bowling shoes, pins, scoreboard, and ball return at the bowling alley.

rather than a plain statement like:

• One checks the bowling shoes, pins, scoreboard, and ball return at the bowling alley.

In learning materials, dictionary-form sentences often describe the target action in this way.