Не будь налобного фонаря, она бы не увидела развилку.

No. Here не будь is not a command like don’t be.

In this sentence, не будь + Genitive is a set conditional expression meaning:

• if it were not for ...
• had there not been ...
• without ...

So:

• Не будь налобного фонаря, она бы не увидела развилку.
• = If it weren’t for the headlamp, she wouldn’t have seen the fork.

Although будь is historically the imperative form of быть, in this pattern it functions as part of a fixed conditional expression.

Because the construction не будь requires the genitive:

• не будь кого? чего?

So:

• налобный фонарь = nominative
• налобного фонаря = genitive singular

This is just how the expression works grammatically. Compare:

• Не будь дождя, мы бы пошли гулять. = If it weren’t for the rain, we would go for a walk.

• Не будь его помощи, я бы не справился. = If it weren’t for his help, I wouldn’t have managed.

Yes, very close.

A fuller, more explicit version would be:

• Если бы не было налобного фонаря, она бы не увидела развилку.

The original sentence is a more compact version:

• Не будь налобного фонаря, она бы не увидела развилку.

So не будь + genitive is an abbreviated conditional structure. It often sounds a bit more literary or compressed than the longer если бы не было... version.

Бы marks the result as hypothetical / unreal.

• она бы не увидела = she would not have seen

This shows that the sentence is talking about something contrary to fact: in reality, she did have the headlamp, and therefore she did see the fork.

Russian conditional sentences often use бы in the result clause, and sometimes also in the condition clause when it is introduced by если:

• Если бы не было фонаря, она бы не увидела развилку.

But in the shorter pattern не будь + genitive, you normally do not add бы to не будь.

Because увидеть is the perfective verb, and here the meaning is a single completed event:

• she caught sight of / noticed the fork

Compare:

• видеть = to see, to be seeing, to have visual perception
• увидеть = to see suddenly, to notice, to catch sight of

In this sentence, the point is not that she was in a state of seeing it, but that she would not have noticed it at that moment. That is why увидела is the natural choice.

Because it is the direct object of увидела.

Dictionary form:

• развилка = fork, branching point, junction

Accusative singular:

• развилку

So:

• увидела что? → развилку

This is standard verb-object grammar.

Развилка usually means a place where one road, path, or route splits into two or more directions.

Depending on context, in English it could be:

• a fork
• a fork in the road/path
• a junction
• a split in the trail

In this sentence, it most likely means a fork in a path, trail, or road that she might have missed without the headlamp.

Literally, it means something like forehead lamp:

• лоб = forehead
• на-лобный = worn on the forehead
• фонарь = lamp / flashlight / torch

So налобный фонарь is a headlamp or head torch.

In the sentence it appears in the genitive singular:

• налобного фонаря

It is about an unreal past result.

The idea is:

• in reality, there was a headlamp
• because of that, she did see the fork
• the sentence imagines the opposite situation: without the headlamp, she would not have seen it

That is why English often translates it with would not have seen.

Yes. Russian word order is flexible.

For example, you could also say:

• Она бы не увидела развилку, не будь налобного фонаря.

This means the same thing, but the emphasis changes slightly:

• sentence-initial Не будь налобного фонаря... foregrounds the condition
• sentence-final ..., не будь налобного фонаря puts the condition after the result, almost like an afterthought or explanation

Both are grammatical.

It is understandable and normal, but it is somewhat more bookish, compressed, or stylistically elevated than the most neutral everyday version.

A more conversational way to say the same thing would often be:

• Если бы не налобный фонарь, она бы не увидела развилку.
• Если бы не было налобного фонаря, она бы не увидела развилку.

So learners should recognize не будь + genitive, but for active speaking, если бы не... may feel easier and more natural at first.

Because Russian often leaves out words that are understood from the pattern.

The full idea is something like:

• Если бы не было налобного фонаря...
• If there had not been a headlamp...

But не будь налобного фонаря compresses all of that into a shorter idiomatic formula. So the meaning of absence/existence is built into the expression itself, even though было is not stated.

Yes, that is an excellent translation.

Possible English versions include:

• If it weren’t for the headlamp, she wouldn’t have seen the fork.
• Had it not been for the headlamp, she would not have seen the fork.
• Without the headlamp, she would not have seen the fork.

The second one matches the slightly compact, literary feel of не будь especially well.