В моей косметичке лежат тушь, помада и маленькое зеркало.

Because after в when it means in / inside, Russian normally uses the prepositional case.

• косметичка = makeup bag / cosmetic bag
• Prepositional singular: в косметичке = in the makeup bag

The possessive word моя also has to match the noun in case, gender, and number:

• nominative: моя косметичка
• prepositional: в моей косметичке

So в моей косметичке means in my makeup bag.

Because моей is the prepositional singular feminine form of моя.

The noun косметичка is:

• feminine
• singular
• here in the prepositional case

So the possessive has to match it:

• моя сумка
• в моей сумке

The same pattern appears with many feminine nouns:

• в моей комнате
• в твоей машине
• в нашей школе

Because the subject is actually a list of several things:

• тушь
• помада
• маленькое зеркало

Together, they form a plural subject, so the verb is plural:

• лежит = lies / is lying / is located (singular)
• лежат = lie / are lying / are located (plural)

Compare:

• В косметичке лежит зеркало. = There is a mirror in the makeup bag.
• В косметичке лежат зеркало и помада. = There are a mirror and a lipstick in the makeup bag.

Russian often uses specific verbs of position where English simply says is / are.

лежать literally means to lie or to be lying, and it is commonly used for things that are lying somewhere.

So:

• В моей косметичке лежат... literally: In my makeup bag lie...
• natural English: In my makeup bag there are... / My makeup bag contains...

Russian often prefers this kind of wording:

• На столе лежит книга. = There is a book on the table.
• В шкафу висят пальто. = There are coats hanging in the wardrobe.
• На полке стоит ваза. = There is a vase standing on the shelf.

Yes. They are the things that lie in the makeup bag, so they are the subject of the sentence and stay in the nominative case.

You can see this clearly with маленькое зеркало:

• зеркало is neuter nominative singular
• маленькое matches it in gender, number, and case

For тушь and помада, the forms here are also nominative singular.

Because зеркало is a neuter singular noun, and adjectives must agree with the noun they describe.

So:

• masculine: маленький
• feminine: маленькая
• neuter: маленькое
• plural: маленькие

Examples:

• маленький стол
• маленькая сумка
• маленькое зеркало
• маленькие вещи

So маленькое зеркало = a small mirror.

They are:

• косметичка — feminine
• тушь — feminine
• помада — feminine
• зеркало — neuter

This matters because gender affects:

• adjective endings
• pronoun forms
• some past-tense verb forms

A couple of useful notes:

• помада is feminine because nouns ending in -а / -я usually are
• зеркало is neuter because nouns ending in -о / -е usually are
• тушь ends in a soft sign -ь, and nouns like that can be masculine or feminine, so its gender has to be learned

Russian has no articles.

So a noun like помада can mean:

• lipstick
• a lipstick
• the lipstick

The exact meaning depends on context.

That is why:

• тушь, помада и маленькое зеркало can naturally mean
  mascara, lipstick, and a small mirror
  or
  the mascara, the lipstick, and the small mirror

English forces you to choose an article, but Russian usually does not.

Yes. Russian word order is more flexible than English word order because case endings show grammatical relationships.

The sentence as given:

• В моей косметичке лежат тушь, помада и маленькое зеркало.

This is natural and neutral.

Other possible orders include:

• Тушь, помада и маленькое зеркало лежат в моей косметичке.
• Лежат в моей косметичке тушь, помада и маленькое зеркало.

These can sound different in emphasis:

• starting with в моей косметичке highlights the location
• starting with the list highlights the objects

But the original sentence is a very normal way to say it.

В means in / inside, while на usually means on / on top of, though Russian usage is sometimes broader than English.

Here, a makeup bag is a container, so Russian uses в:

• в косметичке = in the makeup bag

Compare:

• в сумке = in the bag
• в коробке = in the box
• на столе = on the table
• на полке = on the shelf

So в is the natural choice because the items are inside the cosmetic bag.

Usually yes, or very close. Косметичка refers to a small bag or pouch for cosmetics and toiletry items.

Depending on context, it can be translated as:

• makeup bag
• cosmetic bag
• toiletry bag (sometimes, if the contents are broader)

In this sentence, makeup bag or cosmetic bag is the best fit because the listed items are cosmetics and a mirror.