kanozyo ha sihatu ni girigiri maniatte, hottosite ita.

始発 means the first departure of the day. In this sentence, it most naturally means the first train.

A few useful notes:

• 始発 is often short for 始発電車
• In other contexts, it could mean the first bus, the first subway, etc.
• So 始発に間に合う means to make it in time for the first train

The verb 間に合う commonly uses に to mark the thing or time that someone makes it in time for.

So:

• 始発に間に合う = make it in time for the first train
• 会議に間に合う = make it in time for the meeting
• 締め切りに間に合う = meet the deadline / make the deadline

Here, に does not mean to in a movement sense. It marks the target event or deadline.

ぎりぎり means just barely, at the last possible moment, or by a narrow margin.

So 始発にぎりぎり間に合って means she made the first train, but only just.

This word often gives a feeling of tension or closeness:

• ぎりぎりセーフ = barely safe
• 時間にぎりぎり間に合った = I barely made it on time

間に合う means to be in time, to make it in time, or to meet a deadline / appointment / departure.

Its dictionary form is 間に合う. In the sentence, it becomes 間に合って, which is the て-form.

The て-form is used here to connect this action to the next part of the sentence:

• 間に合って、ほっとしていた
• She made it in time, and then she felt relieved

So 間に合って is not a separate tense by itself here; it is just linking to what follows.

It can suggest more than one relationship, which is very common in Japanese.

Here, 間に合って、ほっとしていた can be understood as:

• She made it in time and was relieved
• She was relieved because she made it in time

Both ideas fit naturally. The て-form often leaves that connection slightly open, and the listener understands it from context.

ほっとする means to feel relieved or to feel a sense of release after worry or tension.

It often has the nuance of:

• whew
• what a relief
• finally, I can relax

So after barely making the first train, she felt relieved.

Because ほっと is commonly treated like a mimetic or sound-symbolic expression, and words like that are often written in kana rather than kanji.

Even though it functions in ほっとする like part of a verb expression, it still keeps that soft, expressive feeling:

• ほっとする = to feel relieved
• ほっとした = felt relieved

Writing it in hiragana is the normal and natural choice.

This is a very good question, because both are possible, but they feel a little different.

• ほっとした = she felt relieved
• ほっとしていた = she was feeling relieved / she was in a relieved state

The form 〜ていた can show:

1. an ongoing action in the past, or
2. a resulting state in the past

Here it is most naturally the second: after making the train, she was in a state of relief.

So ほっとしていた can feel a little more descriptive, as if the speaker is painting the scene and showing her condition at that moment.

は marks 彼女 as the topic of the sentence.

So the sentence is about her:

• 彼女は = as for her / she

It does not necessarily mean strong contrast here, though は can sometimes imply contrast in other contexts. In this sentence, it mainly sets up she as the person being talked about.

Yes, adverbs in Japanese often have some flexibility.

For example, these are also natural:

• 彼女はぎりぎり始発に間に合って、ほっとしていた。
• 彼女は始発に間に合って、ほっとしていた。
  (this removes the barely nuance)

The original placement, 始発にぎりぎり間に合って, is very natural and clearly modifies 間に合って.

Not grammatically. The comma simply makes the sentence easier to read.

So:

• 彼女は始発にぎりぎり間に合って、ほっとしていた。
• 彼女は始発にぎりぎり間に合ってほっとしていた。

Both are understandable, but the comma helps show the break between the two parts:

• making the train
• feeling relieved

In Japanese, punctuation is often lighter and more flexible than in English.