את רוצה את זאת, או את ההיא?

Because את is doing two different jobs here:

• The first את is the pronoun you when speaking to one female. It is pronounced at.
• The other two את words are the direct object marker, pronounced et.

So in:

• את רוצה = you (fem. sg.) want
• את זאת = this one as a direct object
• את ההיא = that one as a direct object

This is a very common source of confusion because the spelling is the same, but the grammar and pronunciation are different.

רוצה here agrees with a singular female subject.

So the sentence is addressed to one woman/girl:

• את רוצה = you (feminine singular) want

Other common forms would be:

• אתה רוצה = you (masculine singular) want
• אתן רוצות = you (feminine plural) want
• אתם רוצים = you (masculine plural) want

In Hebrew, verbs in the present tense show gender and number, but not person as clearly as English does.

In Hebrew, yes/no questions usually do not need an extra helping verb like English do.

English says:

• Do you want this one?

Hebrew simply says:

• את רוצה את זאת?

The sentence becomes a question mainly through:

• intonation in speech
• a question mark in writing
• context

So Hebrew does not need a separate word equivalent to English do here.

They are demonstrative pronouns:

• זאת = this one
• ההיא = that one

They are feminine singular, so they refer to an implied feminine noun, such as:

• שמלה = dress
• חולצה = shirt
• כוס = cup

So the sentence could be understood as something like:

• Do you want this one, or that one? with the noun left unstated.

Because both זאת and ההיא are definite direct objects.

In Hebrew, the direct object marker את is used before a direct object that is definite, for example:

• a noun with the
• a name
• a pronoun
• a demonstrative like this one or that one

So:

• את זאת
• את ההיא

are normal and expected.

More or less, yes.

Both זאת and זו can mean this or this one in the feminine singular. In modern Hebrew:

• זו is often more common in everyday speech
• זאת is also very common, and may sound a bit fuller or slightly more formal in some contexts

So learners will often encounter both.

For example:

• אני רוצה את זו = I want this one
• אני רוצה את זאת = also natural

Both are worth knowing.

Sometimes yes, but in this sentence it is useful to keep it.

Hebrew often omits subject pronouns, but in the present tense, the verb form by itself does not always clearly show the person.
For example, רוצה can mean:

• I want (depending on context)
• you want
• she wants

So את רוצה makes it clear that the speaker is addressing one female.

Without את, the sentence could still work in conversation if the context is obvious, but it would be less explicit.

Because they refer to an implied feminine singular noun.

Hebrew demonstratives must agree in gender and number with the thing they refer to. So if the implied noun is feminine singular, you use feminine singular forms like:

• זאת = this one
• ההיא = that one

If the implied noun were masculine singular, you would use different forms, such as:

• זה = this one
• ההוא = that one

In modern Hebrew, when the noun is stated, the demonstrative usually comes after the noun.

For example:

• את רוצה את החולצה הזאת, או את ההיא?
• Do you want this shirt, or that one?

Or:

• את רוצה את השמלה הזאת, או את השמלה ההיא?

So when the noun is omitted, you get just:

• את זאת
• את ההיא

But when the noun is present, the demonstrative is usually attached after it:

• החולצה הזאת
• השמלה ההיא

A common pronunciation is:

at rotsá et zot, o et hahí?

A few helpful notes:

• את at the beginning = at = you (feminine singular)
• רוצה = rotsá when speaking to a woman
• את before the objects = et
• ההיא = hahí

So even though all three את look identical in writing, the first is pronounced differently from the other two.