В почтовом ящике лежит квитанция за коммунальные услуги.

Because after в meaning in, Russian usually uses the prepositional case for location.

So:

• почтовый → почтовом
• ящик → ящике

That gives в почтовом ящике = in the mailbox.

This is a very common pattern:

• в доме = in the house
• в магазине = in the store
• в ящике = in the box / in the drawer / in the mailbox

So the ending change is showing location, not changing the basic meaning of the words.

Because the subject is singular: квитанция.

Russian verbs in the present tense agree with the subject:

• квитанция лежит = the bill is lying / is located
• квитанции лежат = the bills are lying / are located

Even though коммунальные услуги is plural, that phrase is not the subject. It is part of за коммунальные услуги and means for utility services.

So the verb agrees with квитанция, not with услуги.

Because квитанция is the grammatical subject of the sentence.

In Russian, the thing that is somewhere is often put in the nominative:

• На столе лежит книга. = There is a book on the table.
• В комнате стоит стул. = There is a chair in the room.
• В почтовом ящике лежит квитанция. = There is a bill in the mailbox.

So even though English often starts with there is, Russian usually just uses the noun itself as the subject.

In Russian, verbs like лежать, стоять, and висеть are often used where English simply says is.

• лежать literally means to lie
• but it is also commonly used for objects that are located somewhere horizontally or just resting somewhere

A paper, letter, or bill in a mailbox is naturally described with лежит.

Compare:

• На столе лежит книга. = There is a book on the table.
• У двери стоит чемодан. = There is a suitcase by the door.
• На стене висит картина. = There is a painting on the wall.

So лежит sounds natural in Russian even if English would not literally say lies.

Normally, no. Russian usually does not use есть for simple present-tense there is / there are sentences of location.

English:

• There is a bill in the mailbox.

Natural Russian:

• В почтовом ящике лежит квитанция.

Using есть here would usually sound unnatural or would change the emphasis.

Russian often prefers:

• a location phrase first
• then a verb like лежит, стоит, висит, находится, etc.
• then the noun

So this sentence is a very normal Russian way to express existence/location.

Here за means for in the sense of payment for something.

A квитанция за коммунальные услуги is a bill/receipt for utility services.

This is a common pattern:

• плата за интернет = payment for internet
• счёт за электричество = bill for electricity
• квитанция за квартиру = apartment bill / payment slip for the apartment
• квитанция за коммунальные услуги = utility bill

So за here is not about physical movement behind something. It is the preposition used with payments, charges, and bills.

It is the accusative plural, because за in this meaning takes the accusative.

The phrase is based on the dictionary form:

• коммунальная услуга = utility service

In the plural nominative:

• коммунальные услуги

For inanimate plural nouns, the accusative plural is usually the same as the nominative plural. So:

• nominative plural: коммунальные услуги
• accusative plural: коммунальные услуги

That is why the form does not visibly change here.

Yes, you could. That sentence is grammatical too.

Both of these are correct:

• В почтовом ящике лежит квитанция за коммунальные услуги.
• Квитанция за коммунальные услуги лежит в почтовом ящике.

The difference is mainly focus and information structure.

• В почтовом ящике лежит квитанция... puts the location first and sounds like In the mailbox, there is a utility bill.
• Квитанция... лежит в почтовом ящике puts the bill itself first and sounds more like The utility bill is in the mailbox.

Russian word order is more flexible than English, but it is not random. It helps show what is already known and what is new or important.

Почтовый ящик most commonly means mailbox or letter box.

Literally:

• почтовый = postal / mail
• ящик = box

In modern usage, it can also mean email inbox in some contexts, especially with computers, but in this sentence the physical meaning is clearly intended.

So here в почтовом ящике means in the mailbox.

The stress depends on what is new or important, but a natural neutral pattern would usually place the strongest stress near the end, often on квитанция or on услуги, depending on context:

• В почтовом ящике лежит квитанция за коммунальные услуги.

If the important new information is what is in the mailbox, then квитанция may get stronger stress.

If the important contrast is what kind of bill, then коммунальные услуги may get more emphasis.

This matches the common Russian tendency to put newer or more important information later in the sentence.

Yes, you could say:

• В почтовом ящике находится квитанция за коммунальные услуги.

This is grammatically correct, but it sounds more formal or neutral-descriptive.

Compare the tone:

• лежит = natural, everyday, concrete
• находится = more formal, more abstract, like is located

For a simple everyday statement about a paper in a mailbox, лежит is the more natural choice.