Эта пуговица слишком маленькая для моего пальто.

Because пуговица (button) is a feminine noun in Russian.

The demonstrative this has to agree with the noun in gender, number, and case:

• этот = masculine
• эта = feminine
• это = neuter
• эти = plural

So:

• эта пуговица = this button
• этот стол = this table
• это окно = this window

Since пуговица is feminine, эта is the correct form.

Because маленькая describes пуговица, and adjectives in Russian must agree with the noun they describe.

Here, пуговица is:

• feminine
• singular
• nominative

So the adjective also takes the feminine singular nominative form:

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

So:

• маленькая пуговица = small button
• пуговица маленькая = the button is small

In this sentence, маленькая is part of the predicate after an implied is, but it still stays in the nominative and agrees with пуговица.

In Russian, the verb to be is usually omitted in the present tense.

So Russian says:

• Эта пуговица слишком маленькая... literally: This button too small...

But in natural English, we translate it as:

• This button is too small...

This is completely normal in Russian. Compare:

• Он врач. = He is a doctor.
• Она дома. = She is at home.
• Книга интересная. = The book is interesting.

If you want past or future, then forms of быть appear:

• Эта пуговица была слишком маленькая. = This button was too small.
• Эта пуговица будет слишком маленькая. = This button will be too small.

The preposition для means for, and it requires the genitive case.

So моё пальто (my coat) changes after для to:

• для моего пальто = for my coat

Here:

• для = for
• моего = genitive form of моё / мой
• пальто = coat

A useful rule to remember:

• для + genitive

Examples:

• для меня = for me
• для мамы = for mom
• для нового дома = for the new house
• для моего пальто = for my coat

Because пальто is one of those Russian nouns that are indeclinable, meaning its form stays the same in different cases.

So even though для requires the genitive, пальто still looks like пальто.

What changes instead is the word modifying it:

• nominative: моё пальто
• genitive after для: моего пальто

So the case is still genitive, but only моего visibly changes.

This happens with some borrowed nouns in Russian, especially ones ending in -о, such as:

• пальто = coat
• кино = cinema/movie
• метро = metro

Examples:

• без пальто = without a coat
• в метро = in the metro
• около кинотеатра is different because кинотеатр is declinable, but кино itself is not

Because моё is the nominative form, but after для you need the genitive.

Compare:

• моё пальто = my coat
• для моего пальто = for my coat

Even though пальто is neuter, the form of my still changes for case.

Here are a few neuter forms of мой:

• nominative: моё
• genitive: моего
• dative: моему
• instrumental: моим
• prepositional: моём

So моего is correct because the phrase is in the genitive after для.

Слишком means too, in the sense of more than is acceptable / more than needed.

So:

• слишком маленькая = too small

By contrast, очень just means very:

• очень маленькая = very small

That is an important difference:

• Эта пуговица очень маленькая. = This button is very small.
  (just a description)
• Эта пуговица слишком маленькая для моего пальто. = This button is too small for my coat.
  (it does not work / is unsuitable)

So if the meaning is excessively small, use слишком.

Yes. In this sentence, для is the normal word for for in the sense of intended for / suitable for.

So:

• слишком маленькая для моего пальто = too small for my coat

Russian often uses для + genitive when talking about purpose, suitability, or relation:

• Это для детей. = This is for children.
• Слишком тяжёлый для меня. = Too heavy for me.
• Хороший размер для комнаты. = A good size for the room.

So in your sentence, для expresses that the button is too small in relation to the coat.

Yes, Russian word order is fairly flexible, although some orders sound more natural than others.

The neutral word order here is:

• Эта пуговица слишком маленькая для моего пальто.

You might also hear:

• Для моего пальто эта пуговица слишком маленькая.
  = For my coat, this button is too small.

That version puts extra emphasis on для моего пальто.

In general, the original sentence is the most straightforward and natural if you are simply stating the fact.

Yes. Пуговица is the normal word for a clothing button.

That is exactly the right word for a button on a coat, shirt, jacket, etc.

Be careful, because English button can mean different things, and Russian uses different words depending on context:

• пуговица = clothing button
• кнопка = push-button, button on a device, elevator button, keyboard button

So for a coat, пуговица is correct, not кнопка.

Yes, слишком can feel tricky at first.

A rough pronunciation is:

• sleesh-kum

More carefully:

• слиш sounds a bit like sleesh
• ком is pronounced more like kum because unstressed о is reduced in normal speech

So the whole word is approximately:

• слишком → SLEESH-kum

The stress is on the first syllable:

• СЛИшком

This is a very common Russian word, so it is worth practicing as a whole chunk:

• слишком большой = too big
• слишком дорогой = too expensive
• слишком маленькая = too small

Yes, but it sounds different in style.

• Эта пуговица слишком маленькая для моего пальто is the most natural everyday phrasing.
• Эта пуговица мала для моего пальто is more concise and can sound a bit more formal or literary.

The adjective мал is a short-form adjective, and short forms are often used to express a state or judgment:

• Пальто мне велико. = The coat is too big for me.
• Эта обувь мне мала. = These shoes are too small for me.

So your original sentence is better for a learner to use in normal conversation, but мала is also correct in the right context.