Новые ботинки натирают пятку.

Because новые agrees with ботинки in number, gender, and case.

• ботинки = plural
• the subject is in the nominative
• so the adjective must also be nominative plural

That is why we get:

• новый ботинок = a new boot/shoe
• новые ботинки = new boots/shoes

In this sentence, новые ботинки is the subject: the new shoes are doing the action.

Yes, very often Russian uses the plural for footwear that normally comes as a pair.

• ботинок = one boot/shoe
• ботинки = boots/shoes, often meaning a pair

So Новые ботинки... naturally means something like the new shoes or the new pair of shoes.

Because the subject ботинки is plural.

Russian verbs in the present tense agree with the subject:

• ботинок натирает = one shoe rubs
• ботинки натирают = shoes rub

So натирают is the 3rd person plural form of натирать.

Here натирать means to rub/chafe, especially in the sense that shoes rub against your skin and make it sore.

With shoes, this is a very common use. So the sentence means that the shoes are rubbing the heel and causing discomfort.

It is not about polishing or physically scrubbing something here, even though натирать can have other meanings in other contexts.

Because пятку is the direct object of натирают, so it is in the accusative case.

The dictionary form is:

• пятка = heel

For this feminine noun, the accusative singular changes:

• пятка → пятку

So:

• натирают пятку = rub/chafe the heel

Russian often uses the singular if one heel is meant, or if the speaker is thinking of the problem as affecting the heel area rather than both heels separately.

So Новые ботинки натирают пятку is perfectly natural.

If both heels were meant explicitly, you could say:

• натирают пятки = rub the heels

But the singular is very common in this kind of statement.

Russian often omits possessive words like my with body parts when the owner is obvious from context.

So instead of saying:

• Новые ботинки натирают мою пятку

Russian more naturally says:

• Новые ботинки натирают пятку

It is understood that we are talking about your/my/someone’s heel, depending on context. This is very common in Russian with body parts.

Ботинки is in the nominative plural, because it is the subject of the sentence.

You can see the basic structure like this:

• Новые ботинки = subject
• натирают = verb
• пятку = direct object

So the sentence pattern is:

[Subject] + [Verb] + [Object]

No, Russian word order is fairly flexible, but this version is the most neutral:

• Новые ботинки натирают пятку.

It simply presents the subject first, then the action, then the object.

Other orders are possible for emphasis, for example:

• Пятку натирают новые ботинки.

This can sound more marked, as if focusing on the heel or contrasting what is causing the problem.

For a learner, the given order is the best neutral model.

Натирать is imperfective.

Here that makes sense because the sentence describes an ongoing or repeated problem:

• the shoes rub
• they keep rubbing
• they are causing chafing

The perfective partner is typically натереть, which would refer to a completed result, for example:

• Ботинки натёрли пятку.
  = The shoes rubbed the heel raw / caused a sore spot.

So the sentence with натирают focuses on the process or habitual effect.

Yes, absolutely.

• Новые ботинки натирают пятку. = neutral statement
• Мне новые ботинки натирают пятку. = adds to me, making it more personal/explicit

The dative мне is often used when something affects a person:

• Мне ботинки натирают пятку.

That is also very natural Russian.

A careful pronunciation guide is:

• Но́вые боти́нки натира́ют пя́тку.

Approximate stress:

• НО-вye
• ba-TEEN-kee
• na-tee-RA-yut
• PYAT-ku

The stress is important because Russian vowel pronunciation changes in unstressed syllables.