По мере того как булгур варился, на кухне становилось всё уютнее.

It is a conjunction meaning as, while, or more precisely as... progressively / to the extent that.

In this sentence, it shows that two processes were developing at the same time:

• булгур варился — the bulgur was cooking
• на кухне становилось всё уютнее — the kitchen was becoming cozier and cozier

So по мере того как suggests a gradual parallel change, not just simple simultaneity.

Good question. All three can relate two actions in time, but the nuance is different:

• когда = when
• пока = while
• по мере того как = as, with the idea of gradual change happening alongside something else

So:

• Когда булгур варился... = When the bulgur was cooking...
• Пока булгур варился... = While the bulgur was cooking...
• По мере того как булгур варился... = As the bulgur cooked, ... with a sense that something kept changing more and more during that process.

This phrase is especially common when one thing increases, decreases, changes, or develops over time.

Because вариться is the intransitive/reflexive verb used when something is being cooked / boiling / simmering.

Compare:

• варить булгур = to cook bulgur
  Here someone cooks it; булгур is the object.
• булгур варится = the bulgur is cooking
  Here булгур is the subject, and the process is happening to it.

So варился does not literally mean the bulgur "cooked itself." It is just the normal Russian way to express that food is in the process of cooking.

Here -ся helps turn the verb into a form meaning something like to be cooking / to cook in progress rather than to cook something.

Compare:

• варить = to boil/cook something
• вариться = to boil/cook, to be cooking

In food-related contexts, Russian often uses this reflexive form where English might simply use an intransitive verb:

• Суп варится. = The soup is cooking.
• Рис варится. = The rice is cooking.

So in this sentence, булгур варился is completely natural.

Because the sentence is about an ongoing process, not a completed result.

• варился = imperfective past, was cooking
• a perfective form would focus on completion, something like finished cooking

Since the sentence describes what was happening over time, the imperfective is the right choice. The idea is:

while the bulgur was in the process of cooking, the kitchen kept getting cozier

That ongoing sense is exactly what imperfective verbs are good at.

Here булгур is in the nominative singular because it is the subject of варился.

Its gender is masculine, which is why the past-tense verb is masculine:

• булгур варился

If the noun were feminine, the verb would look different:

• каша варилась

So the ending -лся matches masculine singular.

Because this is an impersonal construction.

Russian often uses neuter singular past tense when there is no clear grammatical subject. Here the sentence does not literally say something was becoming cozier; instead it expresses a general change in atmosphere:

• на кухне становилось всё уютнее = it was getting cozier in the kitchen

English uses a dummy subject it, but Russian does not need one. The verb simply appears in neuter singular:

• становилось

Compare:

• Кухня становилась уютнее. = The kitchen was becoming cozier.
  Here кухня is the subject, so the verb is feminine: становилась.
• На кухне становилось уютнее. = It was becoming cozier in the kitchen.
  No subject, so neuter singular: становилось.

It means cozier and cozier or more and more cozy.

In this pattern:

• уютнее = cozier / more cozy
• всё acts as an intensifier meaning more and more, ever more

So:

• всё лучше = better and better
• всё труднее = harder and harder
• всё уютнее = cozier and cozier

Here всё does not mean everything.

It is the comparative form related to уютный (cozy) / уютно (cozily, cozy), and in sentences like this it functions as a predicative comparative.

That means it is used after a verb like становиться to describe a changing state:

• становилось уютнее = was becoming cozier

For a learner, the most useful point is this: after становиться, comparative forms like лучше, хуже, теплее, уютнее are very common.

Because на кухне is the normal, idiomatic way to say in the kitchen.

Russian often uses на with certain places understood as functional spaces:

• на кухне = in the kitchen
• на работе = at work
• на улице = outside / on the street

В кухне is much less natural here. It may appear in special contexts, for example when talking about the room as part of a building layout, but in ordinary speech на кухне is what you want.

Because the sentence has two clauses:

1. По мере того как булгур варился — subordinate clause
2. на кухне становилось всё уютнее — main clause

Russian separates them with a comma, just as English often does in a sentence like:

As the bulgur cooked, the kitchen became cozier and cozier.

So the comma marks the boundary between the subordinate clause and the main clause.

Yes. Russian word order is flexible, though the original sounds very natural.

Original:

• По мере того как булгур варился, на кухне становилось всё уютнее.

Possible rearrangement:

• На кухне становилось всё уютнее по мере того как булгур варился.

The meaning stays basically the same, but the original version feels smoother because it sets up the background process first and then gives the result or accompanying change.

Yes. A very natural alternative would be:

Чем дольше варился булгур, тем уютнее становилось на кухне.

That means:

The longer the bulgur cooked, the cozier the kitchen became.

The difference is mostly stylistic:

• по мере того как = as, emphasizing gradual parallel development
• чем... тем... = the more/the longer..., the more..., emphasizing a direct correlation

Both are good, but the original sentence is a bit softer and more descriptive.