אם אסיים את שיעורי הבית מוקדם, אצייר תמונה קטנה על דף חדש.

Because the sentence talks about a future situation:

• אם אסיים... = if I finish...
• אצייר... = I will draw...

In Hebrew, a real future condition like this often uses the future tense in both parts of the sentence. That is different from English, where we usually say If I finish... I will draw... and not If I will finish...

So this is a very normal Hebrew pattern:

• אם + future
• future

Hebrew verbs usually already show the subject, so אני is often unnecessary.

• אסיים already means I will finish
• אצייר already means I will draw

So the subject I is built into the verb form. You could add אני for emphasis, but it is not needed in a neutral sentence.

אסיים is the 1st person singular future form of the verb לסיים (to finish).

So:

• לסיים = to finish
• אסיים = I will finish

The prefix א- often marks I in the future tense.

אצייר is the 1st person singular future form of לצייר (to draw / to paint).

So:

• לצייר = to draw
• אצייר = I will draw

Again, the א- at the beginning shows I in the future tense.

את marks a definite direct object in Hebrew.

Here, שיעורי הבית means the homework, which is definite, so Hebrew uses את:

• אסיים את שיעורי הבית

A helpful rule:

• If the direct object is definite, Hebrew usually uses את
• If it is indefinite, it usually does not

Compare:

• אני קורא ספר = I am reading a book
• אני קורא את הספר = I am reading the book

This is just how Hebrew expresses the idea. שיעורי הבית is literally something like the house lessons / home assignments, and it is treated as a plural expression.

Breakdown:

• שיעורים = lessons / assignments
• שיעורי = lessons of...
• הבית = the house / home

Together:

• שיעורי הבית = homework

So even though English uses a singular-looking mass noun (homework), Hebrew uses this plural construct phrase.

Because it is in the construct state.

In Hebrew, when one noun is linked to another noun in an of relationship, the first noun often changes form. This is called סמיכות (construct state).

So:

• שיעורים = lessons
• שיעורי הבית = lessons of the house / homework

This pattern is very common in Hebrew.

Because here מוקדם is functioning like an adverb, meaning early.

It describes when the action happens:

• אסיים ... מוקדם = I will finish ... early

Since it is not describing a noun here, it does not need to agree with a noun in gender or number.

In Hebrew, adjectives usually come after the noun they describe.

So:

• תמונה קטנה = a small picture

This is the normal Hebrew order:

• noun + adjective

Also, the adjective must agree with the noun:

• תמונה is feminine singular
• קטנה is feminine singular

That is why it is קטנה and not קטן.

Hebrew adjectives must agree with the noun in gender and number.

In this sentence:

• תמונה is feminine singular, so the adjective is קטנה
• דף is masculine singular, so the adjective is חדש

So:

• תמונה קטנה = small picture
• דף חדש = new page/sheet

A learner should always ask: what is the gender and number of the noun?

Here על means on.

• על דף חדש = on a new sheet / on a new page

Hebrew uses על naturally for writing or drawing on a surface such as paper.

So:

• לכתוב על דף = to write on a sheet/page
• לצייר על דף = to draw on a sheet/page

It can mean either, depending on context.

• דף can be page
• It can also be sheet of paper

In this sentence, both a new page and a new sheet fit well. The exact choice depends on the context the learner was given.

Yes. Hebrew can also put the main clause first:

• אצייר תמונה קטנה על דף חדש אם אסיים את שיעורי הבית מוקדם.

This still means the same thing:

• I will draw a small picture on a new sheet if I finish my homework early.

The original order is very natural, especially when the speaker wants to present the condition first.

In standard writing, a comma is commonly used when the sentence begins with a conditional clause:

• אם אסיים את שיעורי הבית מוקדם, אצייר תמונה קטנה על דף חדש.

This is similar to English punctuation with an opening if clause.

In very informal writing, punctuation may be less strict, but the comma is standard and helpful.

Yes. A common alternative is לגמור:

• אם אגמור את שיעורי הבית מוקדם...

This is also natural and common in speech.
Very roughly:

• לסיים often sounds a bit more neutral or standard
• לגמור is also very common, sometimes a bit more everyday/colloquial depending on context

In your sentence, אסיים is perfectly natural.

Usually, yes: אם commonly means if.

In this sentence:

• אם אסיים... = if I finish...

It introduces a condition. This is one of the most common uses of אם in Hebrew.

A natural pronunciation would keep the main stress on the final stressed syllables of the words, for example:

• אִם אֲסַיֵּים אֶת שִׁעוּרֵי הַבַּיִת מוּקְדָּם, אֲצַיֵּיר תְּמוּנָה קְטַנָּה עַל דַּף חָדָשׁ.

A few points learners often notice:

• אסיים sounds like a-sa-YEM
• אצייר sounds like a-tsa-YER
• שיעורי הבית has connected, flowing pronunciation in natural speech

Even if your pronunciation is not perfect, getting the future forms and word order right is more important at first.

The sentence follows this pattern:

• אם
  • future verb + object + adverb,
    future verb + object + prepositional phrase

More specifically:

• אם
• אסיים
• את שיעורי הבית
• מוקדם
• אצייר
• תמונה קטנה
• על דף חדש

So it is a very useful model for making your own Hebrew sentences:

• If X happens, I will do Y.