Корка стала тёмной вплоть до того, что надрез почти исчез.

Because after the verb стать in the meaning to become, Russian normally uses the instrumental case for the resulting state.

• тёмная = nominative feminine singular
• тёмной = instrumental feminine singular

So:

• Корка стала тёмной = The crust became dark

This is a very common pattern:

• Он стал врачом = He became a doctor
• Она стала известной = She became famous
• Небо стало серым = The sky became gray

You may sometimes see nominative after стать in some contexts, but instrumental is the standard choice here.

Вплоть до того, что means something like:

• to the point that
• so much so that
• to such an extent that

It introduces an extreme result.

So in this sentence:

• Корка стала тёмной вплоть до того, что надрез почти исчез
• The crust became so dark that the score/cut almost disappeared

This expression is a bit more emphatic than a simple так... что or настолько... что. It suggests the change went very far.

Надрез means a cut, slit, or score mark made on the surface of something.

In this sentence, it most likely refers to the cut made on dough or bread before baking. So if the crust got very dark, that cut became hard to see.

Related words:

• резать = to cut
• разрез = a cut / incision / cross-section depending on context
• надрез = a cut made into the surface, often not all the way through

For bread, надрез is often best understood as the scoring mark.

Исчез is the past masculine singular form of the perfective verb исчезнуть (to disappear).

Here it is used because the sentence talks about a resulting change:

• the crust darkened so much
• that the cut almost disappeared

The perfective verb focuses on the result or completion of the change.

Compare:

• исчезал = was disappearing / used to disappear / disappeared repeatedly or gradually in context
• исчез = disappeared

Even with почти (almost), perfective is still natural:

• почти исчез = almost disappeared

Because the normal modern perfective verb is исчезнуть, but its past tense is irregular in usage:

• infinitive: исчезнуть
• past masculine: исчез
• past feminine: исчезла
• past neuter: исчезло
• plural: исчезли

So исчезнул does exist historically and can occasionally be heard, but исчез is the normal standard form.

Корка is in the nominative case because it is the subject of the sentence.

• Корка = crust
• стала = became

So корка is the thing doing the becoming.

Then тёмной is in the instrumental because it describes what the crust became.

Structure:

• Корка — subject, nominative
• стала — verb
• тёмной — predicate adjective after стать, instrumental

Here того is the genitive singular form of то (that).

The expression is built like this:

• до requires the genitive
• so то becomes того

That is why we get:

• до того = literally up to that
• вплоть до того, что = to the point that / so much so that

You do not need to translate each word literally every time. It is best learned as a fixed expression.

Yes. Very similar alternatives are possible:

• Корка стала настолько тёмной, что надрез почти исчез.
• Корка стала такой тёмной, что надрез почти исчез.
• Корка так потемнела, что надрез почти исчез.

These all mean roughly the same thing.

However:

• вплоть до того, что sounds a bit more emphatic
• it highlights an extreme result
• it can feel slightly more bookish or formal than the simplest options

Because it agrees with корка, which is a feminine singular noun.

Dictionary form:

• тёмный = masculine
• тёмная = feminine nominative
• тёмное = neuter
• тёмные = plural

But after стать, we need the instrumental form, so feminine singular becomes:

• тёмной

So the feminine comes from agreement with корка, and the exact ending comes from the instrumental case.

Yes, Russian word order is flexible, though the neutral order here is very natural:

• Корка стала тёмной вплоть до того, что надрез почти исчез.

You could also say:

• Надрез почти исчез: корка стала тёмной вплоть до того.
  This is less natural and sounds more marked or literary.
• Корка вплоть до того стала тёмной, что надрез почти исчез.
  This is awkward and not the usual placement.

In practice, the original word order is the best choice because the phrase вплоть до того, что works smoothly just before the result clause.

Yes, it is very natural.

• почти = almost
• исчез = disappeared

So:

• надрез почти исчез = the cut almost disappeared

This is a common Russian pattern:

• почти забыл = almost forgot
• почти упал = almost fell
• почти сломался = almost broke

In this sentence it means the cut did not fully vanish, but became very hard to see.

Yes, and it would be very natural:

• Корка потемнела вплоть до того, что надрез почти исчез.

Difference:

• стала тёмной = became dark
• потемнела = darkened / became darker

Both work well.
Потемнела focuses more directly on the change itself, while стала тёмной describes the resulting state.

The main stresses are:

• ко́рка
• стала
• тёмной
• вплоть
• до того́, что
• надре́з
• почти́
• исче́з

A learner may especially want to notice:

• тёмной has ё, which is always stressed
• надре́з is stressed on the second syllable
• исче́з is stressed on the second syllable

If you pronounce ё correctly, it helps a lot with sounding natural.