אם את רוצה, אני יכולה לקנות גם פיצה בדרך לפארק.

Because both the person being addressed and the speaker are female.

• את = you (singular, feminine)
• אני יכולה = I can / I am able said by a female speaker

So the sentence is something a woman says to another woman.

If you were speaking to a man, you would say:

• אם אתה רוצה, אני יכולה...

If the speaker were male, it would be:

• אם את רוצה, אני יכול...

Hebrew marks gender much more often than English does.

In unpointed Hebrew spelling, some masculine and feminine forms look identical in writing.

So:

• רוצה can be rotze = masculine singular
• רוצה can also be rotza = feminine singular

The spelling is the same, but the pronunciation changes. Here, because the subject is את, it must be read as the feminine form: rotza.

This is very common in everyday Hebrew, since most texts are written without vowel marks.

Because Hebrew often uses the present tense in a natural, conversational way for if you want.

• אם את רוצה = if you want
• אם תרצי = also possible, but can sound a little more like if you decide you want / if you will want

In everyday offers like this, אם את רוצה is very natural and common.

This is the Hebrew way to say can buy.

• יכולה = can / able to (feminine singular)
• לקנות = to buy

So:

• אני יכולה לקנות = I can buy

Hebrew often uses:

• יכול / יכולה / יכולים / יכולות
  • infinitive

Examples:

• אני יכול ללכת = I can go
• היא יכולה לעזור = She can help

Here the ל is part of the infinitive, like English to in to buy.

• קונה = buys / buying
• לקנות = to buy

So in this sentence:

• יכולה לקנות = can buy

This ל is not the same as the preposition to in a phrase like to the park, even though it looks the same. Hebrew uses the same letter for several jobs, and context tells you which one it is doing.

It could sometimes be omitted in context, but here אני is helpful and natural.

Why? Because Hebrew present-tense forms like יכולה show:

• gender
• number

but not person clearly enough on their own.

So יכולה could mean:

• I can (female)
• you can (female singular)
• she can

Since the sentence starts with את (you), adding אני makes the subject switch very clear:

• אם את רוצה, אני יכולה...
  If you want, I can...

Without אני, the sentence would be less clear.

גם means also / too.

In this sentence, placing it before פיצה makes pizza the added item:

• לקנות גם פיצה = buy pizza too / also buy pizza

This suggests pizza is being added to something already understood from the conversation.

Compare:

• אני גם יכולה לקנות פיצה = I can also buy pizza
  Here the emphasis is a bit more on I can also do that

• אני יכולה לקנות גם פיצה = I can buy pizza too
  Here the emphasis is more on pizza being an additional thing

Both are possible, but the original placement is very natural.

Because Hebrew does not have an indefinite article like English a/an.

So:

• פיצה can mean pizza or a pizza
• הפיצה means the pizza

That means Hebrew often leaves definiteness to context unless it needs to be specific.

Here בדרך means on the way.

It is an idiomatic expression:

• בדרך ל... = on the way to...

So:

• בדרך לפארק = on the way to the park

In unpointed writing, בדרך could in theory be read in different ways, but in this sentence the meaning is clearly ba-derekh = on the way.

This is a very useful chunk to remember as one expression:

• בדרך הביתה = on the way home
• בדרך לעבודה = on the way to work

Great question. The definite article ה often combines with prepositions.

So:

• ל + הפארק becomes לפארק

In fully pointed Hebrew, the pronunciation would show the difference more clearly, but in normal unpointed spelling it all looks like לפארק.

So this written form can represent:

• le-park = to a park
• la-park = to the park

Context tells you which one is meant. In your sentence, the meaning is to the park.

Yes, Hebrew word order is somewhat flexible, but different orders can change the emphasis.

The original:

• אם את רוצה, אני יכולה לקנות גם פיצה בדרך לפארק.

is very natural and neutral.

You could also say:

• אני יכולה לקנות גם פיצה בדרך לפארק, אם את רוצה.

That puts the main offer first and the if you want part afterward, almost like I can also buy pizza on the way to the park, if you want.

So the original order is not the only possible one, but it is a very normal way to phrase this kind of offer.

Here are the main variations:

• to one woman, spoken by a woman:
  אם את רוצה, אני יכולה לקנות גם פיצה בדרך לפארק.

• to one man, spoken by a woman:
  אם אתה רוצה, אני יכולה לקנות גם פיצה בדרך לפארק.

• to one woman, spoken by a man:
  אם את רוצה, אני יכול לקנות גם פיצה בדרך לפארק.

• to one man, spoken by a man:
  אם אתה רוצה, אני יכול לקנות גם פיצה בדרך לפארק.

So when learning Hebrew, it helps to track two separate things:

1. Who are you talking to?
2. Who is speaking?

Both can affect the form of the sentence.