Utleieskoene ligger i bowlinghallen.

Because Norwegian normally writes compound nouns as a single word.
Here, utleie + sko becomes utleiesko = rental shoe, and then the definite plural ending is added:

utleiesko + -ene = utleieskoene

This is very typical in Norwegian. Where English often uses several words, Norwegian often packs them into one noun.

A useful breakdown is:

• utleie = rental / renting out
• sko = shoe / shoes
• -ene = the definite plural ending

So grammatically, utleieskoene means the rental shoes.

Also, the last part of a Norwegian compound is the main noun. So utleiesko is a kind of shoe, not a kind of rental.

In Norwegian, definiteness is usually shown by an ending attached to the noun rather than by a separate word.

So instead of saying:

• the shoes

Norwegian often says:

• skoene = the shoes

In this sentence:

• utleieskoene = the rental shoes
• bowlinghallen = the bowling hall / the bowling alley

This is one of the biggest differences from English.

Yes. Sko is one of those Norwegian nouns where the indefinite singular and indefinite plural have the same form.

So:

• en sko = a shoe
• sko = shoes
• skoene = the shoes

Context tells you whether sko is singular or plural when there is no article in front of it.

Norwegian often uses position verbs where English just uses is/are.

Here, ligger literally means lies / is lying, but in normal Norwegian it is also commonly used to say that something is located somewhere, especially when the thing is thought of as resting or lying there.

So:

• Skoene ligger i hallen = The shoes are in the hall

If you used er, it would usually sound less natural here. Norwegian prefers:

• ligger for things lying/resting
• står for things standing
• henger for things hanging

Shoes are naturally understood as something that lies somewhere, so ligger is the normal choice.

Because i is used for being inside an enclosed place.

So:

• i bowlinghallen = in the bowling hall / inside the bowling alley

Using på would usually not fit this physical meaning. På is often used with surfaces, islands, some institutions, and certain set expressions, but for a building or hall that something is physically inside, i is the expected preposition.

Because bowlinghall is in the singular definite form.

The pattern is:

• en bowlinghall = a bowling hall
• bowlinghallen = the bowling hall

The ending -en is the common singular definite ending for many masculine/common-gender nouns in Bokmål.

So just like skoene means the shoes, bowlinghallen means the bowling hall.

The sentence follows normal Norwegian main-clause word order:

Utleieskoene + ligger + i bowlinghallen
subject + verb + place

So it is a straightforward statement.

If you move the place expression to the front, Norwegian still keeps the verb in second position:

• I bowlinghallen ligger utleieskoene.

That verb-second pattern is very important in Norwegian main clauses.

You can, but it changes the meaning.

• Utleieskoene ligger i bowlinghallen = the rental shoes are in the bowling hall
  This refers to specific rental shoes.

• Utleiesko ligger i bowlinghallen = more like rental shoes are in the bowling hall or there are rental shoes in the bowling hall
  This sounds more indefinite or generic.

So if the sentence is talking about a particular set of rental shoes, utleieskoene is the natural form.

More or less, yes. Literally, bowlinghall is bowling hall, and in real usage it can refer to the place where you go bowling—the kind of place English often calls a bowling alley.

So even if the Norwegian word looks a bit different from the usual English expression, the meaning in context is the same kind of place.