На чашке появилась маленькая трещина, и я больше не наливаю в неё кипяток.

Because the crack is understood as being on the cup / in the cup’s surface or body, not inside the cup’s interior where liquid goes.

• на + prepositional often means on the surface of something
• в + prepositional means in / inside something

So:

• На чашке появилась трещина = a crack appeared on the cup
• В чашке would sound like something is inside the cup

With cracks, Russian often uses на when talking about the outside surface or object as a surface-bearing thing.

In the past tense, Russian verbs agree in gender and number with the subject.

The subject here is трещина (crack), which is:

• feminine
• singular

So the verb must also be feminine singular in the past:

• появился = masculine
• появилась = feminine
• появилось = neuter
• появились = plural

Even though трещина comes after the verb, it is still the subject, so the verb agrees with it.

Because it is the subject of the clause.

In На чашке появилась маленькая трещина:

• появилась = appeared
• маленькая трещина = the thing that appeared

The thing doing the grammatical action of appearing is the subject, so it stays in the nominative:

• маленькая — feminine nominative singular
• трещина — feminine nominative singular

Russian often allows the verb to come before the subject, especially when introducing something new:

• Появилась маленькая трещина
• literally: Appeared a small crack
• natural Russian word order, even though English prefers A small crack appeared

Больше не means no longer, not anymore, or not any longer.

So:

• я больше не наливаю = I no longer pour
• I don’t pour anymore

A useful way to think about it:

• не = not
• больше не = not anymore / no longer

Examples:

• Я больше не курю. = I don’t smoke anymore.
• Он больше не работает здесь. = He no longer works here.

It often suggests that the action used to happen before, but now it has stopped.

Наливаю is the imperfective verb, and it fits because the speaker is talking about a general repeated action / habit:

• я больше не наливаю в неё кипяток = I no longer pour boiling water into it

This is not about one single future action. It is about a usual practice that has stopped.

Compare:

• Я больше не наливаю в неё кипяток.
  = I don’t pour boiling water into it anymore.
  (general habit, repeated action)

• Я больше не налью в неё кипяток.
  = I won’t pour boiling water into it anymore / again.
  (more like a decision about a specific future act)

So imperfective present in Russian is very often used for habits, routines, and general truths.

Because в can take different cases depending on meaning:

• в + accusative = into
• в + prepositional = in / inside

Here the idea is movement of the water into the cup, so Russian uses the accusative:

• в неё = into it

Compare:

• В ней чай. = There is tea in it.
  (в ней = location)
• Я наливаю чай в неё. = I pour tea into it.
  (в неё = direction)

Since чашка is feminine, the pronoun is feminine too:

• nominative: она
• accusative after в for direction: неё

Russian, like English, often uses a pronoun to avoid repeating a noun.

So after mentioning чашке, the next clause naturally uses неё = it:

• ...и я больше не наливаю в неё кипяток
• ...and I no longer pour boiling water into it

If you repeated the noun, it would still be grammatical:

• ...и я больше не наливаю в чашку кипяток

But using в неё sounds more natural because the cup has just been mentioned.

Кипяток means boiling water as a noun. It is a very common everyday word.

• кипяток = boiling water
• кипящая вода = literally water that is boiling

In many ordinary situations, кипяток is the more natural choice:

• Налить кипяток в чашку = to pour boiling water into a cup

Кипящая вода can sound a bit more descriptive or literal, especially if you mean water that is actively boiling at that moment.

So in this sentence, кипяток is exactly the normal word you would expect.

It actually is in the accusative case, but for an inanimate masculine noun, the accusative often looks exactly like the nominative.

Here, кипяток is the direct object of наливаю, so it should be accusative:

• nominative: кипяток
• accusative: кипяток

Same form, different function.

This is normal for many masculine inanimate nouns in Russian. Compare:

• Я вижу стол. = I see a table.
  (стол is accusative here, but looks like nominative)

So the form does not change visibly, but the case is still accusative.

Yes, Russian word order is flexible, and this sentence is arranged in a very natural way.

Current order:

• На чашке появилась маленькая трещина, и я больше не наливаю в неё кипяток.

This structure works well because:

1. На чашке sets the scene first
2. появилась маленькая трещина introduces new information
3. the second clause gives the consequence

Russian often places location first and then introduces what appeared there. That is why На чашке появилась... sounds natural.

You could also say:

• Маленькая трещина появилась на чашке...

This is grammatical too, but it shifts the focus a bit more toward маленькая трещина.

So the original order is not random; it reflects typical Russian information flow.

Yes, but it is not exactly the same nuance.

• На чашке появилась маленькая трещина
  = A small crack appeared on the cup.
  This focuses on the result: there is now a visible crack.

• Чашка треснула
  = The cup cracked.
  This focuses more on the event of cracking.

The original sentence is more precise because it says the crack is small and mentions it directly:

• маленькая трещина

That makes it especially suitable if the speaker is explaining why they no longer use the cup for boiling water.