مع أنني متعبة، لا أزال أنظر في الدفتر حتى أفهم الدرس جيدا.

مع أنني means although I... / even though I...

It is built from:

• مع أن = although / even though
• ني = me / I attached to أن

So:

• مع أنني متعبة = although I am tired

You can think of مع أن as a fixed connector that introduces a concessive clause.

Arabic usually does not use a present-tense verb meaning am/is/are in sentences like this.

So:

• أنا متعبة literally looks like I tired
• but it means I am tired

The same thing happens after أن:

• أنني متعبة = that I am tired

This is a normal feature of Arabic nominal sentences in the present tense.

Because the speaker is feminine.

• متعبة = tired, said by/about a female
• متعب = tired, said by/about a male

So this sentence is being said by a woman or girl. If a male were speaking, it would be:

• مع أنني متعب، لا أزال...

Notice that the first-person verbs like أنظر and أفهم do not show gender, but the adjective متعبة does.

Because لا أزال is a fixed expression meaning I still... / I continue to...

With verbs from زال, negative particles often create this idea of continued state:

• ما زال = still
• لا يزال = still
• لم يزل = still has not ceased

So:

• لا أزال أنظر = I am still looking

Even though لا often means not, in this expression the whole phrase should be learned together.

It means I am still looking or I continue to look.

Here:

• لا أزال gives the idea of continuation
• أنظر is the action that is continuing

So the sentence is not just saying I look. It is saying the action is ongoing:

• I am still looking in the notebook

This is one common way Arabic expresses still.

Because the preposition changes the nuance.

• نظر إلى = look at
• نظر في = look into, examine, consult, look through

So:

• أنظر في الدفتر suggests I am looking through the notebook / checking the notebook / reading in the notebook
• أنظر إلى الدفتر would sound more like I am looking at the notebook with my eyes directed toward it

In this sentence, في fits better because the person is studying from the notebook, not just staring at it.

Yes. After حتى, the imperfect verb is often in the subjunctive when it means until or so that.

So in fully vocalized Arabic, it would be:

• حتى أفهمَ

But in normal unvocalized writing, that final vowel is not shown, so it appears simply as:

• حتى أفهم

So the spelling looks the same, but the grammar is different underneath.

In this sentence, حتى أفهم means:

• until I understand
• or so that I understand

It can feel like either, depending on how you interpret the sentence.

• until I understand the lesson well
• so that I understand the lesson well

Both fit the context. The speaker keeps looking in the notebook, and the endpoint or goal is understanding the lesson.

So حتى here combines:

• an endpoint idea
• and a purpose/result idea

That is very common in Arabic.

الدرس is the direct object of أفهم.

So:

• أفهم = I understand
• الدرس = the lesson

Together:

• أفهم الدرس = I understand the lesson

In fully vocalized Arabic, it would be الدَّرسَ because it is in the accusative case, but short vowels are usually omitted in normal writing.

No. Here جيدا means well, so it is functioning as an adverb, not as an adjective describing الدرس.

So:

• أفهم الدرس جيدا = I understand the lesson well

Why it is not an adjective of الدرس:

• If it were describing الدرس, it would need to match it in definiteness
• الدرس is definite
• جيدا is indefinite

So this does not mean the good lesson

If you wanted the good lesson, you would say:

• الدرس الجيد

Also, in fully vocalized spelling, you would usually see:

• جيدًا

But in everyday Arabic writing, the short vowels are often left out, so جيدا is very common.

Yes, definitely.

A few natural variations are:

• مع أني متعبة...
• مع أنني متعبة...

Both are used, and both mean although I am tired.

Also:

• ما زلت أنظر في الدفتر...
• لا أزال أنظر في الدفتر...

Both mean I am still looking in the notebook...

The version in your sentence is a good formal MSA sentence, but Arabic often allows more than one natural way to express the same idea.