Było tyle dymu, że nie widziałam drzwi.

Because było is being used in an impersonal there was / there were type of structure.

In Było tyle dymu..., Polish is not really saying the smoke was.... It is saying something more like There was so much smoke...

With this kind of quantity expression, Polish very often uses neuter singular było, even if the noun itself has another grammatical gender.

So:

• Był dym = There was smoke / Smoke was present
• Było dużo dymu = There was a lot of smoke
• Było tyle dymu = There was so much smoke

That is why było is the natural form here.

Because after tyle meaning so much / that much / so many, the following noun normally goes in the genitive.

So:

• dym = nominative
• dymu = genitive

That gives:

• tyle dymu = so much smoke

This is very common in Polish with words of quantity, for example:

• dużo wody = a lot of water
• mało czasu = little time
• tyle ludzi = so many people

So tyle dymu is the expected grammar.

Here tyle means so much.

By itself, tyle can mean:

• this much
• that much
• so much
• so many

The exact meaning depends on context.

In the pattern tyle... że..., it usually means so much... that...

So:

• Było tyle dymu, że... = There was so much smoke that...

This is a very common Polish pattern.

Że here means that in the sense of so... that...

The structure is:

• tyle..., że... = so much..., that...
• tak..., że... = so..., that...

So the sentence works like this:

• Było tyle dymu = There was so much smoke
• że nie widziałam drzwi = that I couldn’t see the door

Together:

• Było tyle dymu, że nie widziałam drzwi.

Because Polish past tense agrees with the speaker’s gender.

• widziałam = I saw / I could see, said by a woman
• widziałem = I saw / I could see, said by a man

So if a male speaker said this sentence, it would be:

• Było tyle dymu, że nie widziałem drzwi.

This is one of the important differences between Polish and English: in Polish, past tense often shows the speaker’s gender.

Literally, nie widziałam means I did not see.

But in context, English often prefers couldn’t see because the sentence describes an inability caused by the smoke.

So:

• literal meaning: I didn’t see the door
• natural English meaning in context: I couldn’t see the door

Both ideas are close here, but the second is usually the better translation.

Yes. Drzwi is one of those Polish nouns that are plural-only in form.

Grammatically, it behaves like a plural noun, but it can refer to:

• a door
• doors

depending on context.

So in this sentence, drzwi most naturally means the door.

This is similar to a few other Polish nouns that exist only in plural form, even when English uses a singular word.

Because Polish usually drops subject pronouns when they are not needed.

The ending of the verb already tells you the person, and in the past tense it can also tell you gender.

So:

• widziałam already means I saw / I could see and also shows that the speaker is female.

Because of that, adding ja is usually unnecessary unless you want emphasis.

So:

• nie widziałam drzwi = I couldn’t see the door
• ja nie widziałam drzwi = I couldn’t see the door with extra emphasis on I

Yes, Polish word order is fairly flexible, although the original sentence is very natural.

The standard version:

• Było tyle dymu, że nie widziałam drzwi.

A reordered version might be possible for emphasis, but the original is the most neutral and natural for a learner to use.

In general, Polish changes word order more freely than English, but not every alternative sounds equally normal. Here, the given version is a very good default pattern to remember:

• Było tyle X, że... = There was so much X that...

Yes, very easily. This is a useful model sentence.

Pattern:

• Było tyle + genitive noun, że...
• There was so much / so many + noun, that...

Examples:

• Było tyle hałasu, że nie mogłem spać.
  There was so much noise that I couldn’t sleep.

• Było tyle ludzi, że nie mogliśmy wejść.
  There were so many people that we couldn’t enter.

• Było tyle pracy, że wróciłam późno.
  There was so much work that I came back late.

So this sentence is useful not only by itself, but also as a grammar pattern you can reuse.