אני לא רוצה את זאת; אני מעדיפה את השמלה האדומה.

Here את is the direct object marker, not the preposition meaning with.

Hebrew uses את before a direct object that is definite or specific. In this sentence:

• זאת = this/that one (a specific one)
• השמלה האדומה = the red dress (definite because of ה־)

So both take את.

Compare:

• אני רוצה שמלה אדומה = I want a red dress.
  No את, because the object is indefinite.
• אני רוצה את השמלה האדומה = I want the red dress.
  את is required.

זאת means this one or that one.

It is feminine singular, which tells you the thing being referred to is feminine. In this sentence, that makes sense because שמלה (dress) is a feminine noun.

If the thing were masculine, Hebrew would usually use זה instead:

• אני לא רוצה את זה = I don't want this/that one. (masculine)

Both זאת and זו can mean the feminine this/that in Modern Hebrew.

Very roughly:

• זאת = the fuller form
• זו = also very common, especially in everyday use

In many situations, they are interchangeable.

Examples:

• אני רוצה את זאת
• אני רוצה את זו

Both can mean I want this one / that one.

With a noun:

• השמלה הזאת
• השמלה הזו

Both mean this dress / that dress, depending on context.

Often, it can mean either one.

Unlike English, Modern Hebrew does not always sharply distinguish this and that in the basic demonstratives. Context usually makes the meaning clear.

So זאת may be understood as:

• this one
• that one

If Hebrew wants to be more explicit, it can use other wording, such as ההיא for that one, or add context words like כאן (here) or שם (there).

Because of מעדיפה.

מעדיפה is the feminine singular present-tense form of to prefer.

So the sentence is being said by a woman or girl:

• אני מעדיפה = I prefer (female speaker)

If the speaker were male, it would be:

• אני מעדיף = I prefer (male speaker)

A useful detail: רוצה is written the same way for masculine and feminine in unpointed Hebrew, so by itself it does not clearly show gender in normal spelling. But מעדיפה does.

So:

• אני לא רוצה את זאת; אני מעדיפה את השמלה האדומה. = female speaker
• אני לא רוצה את זאת; אני מעדיף את השמלה האדומה. = male speaker

Because in Hebrew, adjectives normally come after the noun they describe.

So:

• שמלה אדומה = a red dress
• השמלה האדומה = the red dress

This is different from English, where adjectives usually come before the noun.

Because Hebrew adjectives must agree with the noun not only in gender and number, but also in definiteness.

So if the noun is definite, the adjective must also be definite.

• שמלה אדומה = a red dress
• השמלה האדומה = the red dress

You cannot normally say השמלה אדומה if you mean the red dress as a noun phrase.
That would instead mean the dress is red in a sentence like a predicate.

Because שמלה is a feminine singular noun, and the adjective must match it.

So:

• אדום = red, masculine singular
• אדומה = red, feminine singular

Examples:

• ספר אדום = a red book
• שמלה אדומה = a red dress

That same agreement is why the sentence has השמלה האדומה and not השמלה האדום.

Hebrew does not always need an explicit but.

The contrast can simply be understood from the two clauses side by side, and the punctuation helps show that:

• אני לא רוצה את זאת; אני מעדיפה את השמלה האדומה.

English often prefers but, but Hebrew can be more compact here.

You could also say:

• אני לא רוצה את זאת, אבל אני מעדיפה את השמלה האדומה.

That means the same thing, just with אבל (but).

Sometimes yes, but keeping it is very common and natural.

In present-tense Hebrew, the verb often does not clearly show the person the way English does, so speakers frequently say the subject pronoun:

• אני לא רוצה...
• אני מעדיפה...

In casual speech, the second אני might be omitted if the subject is obvious:

• אני לא רוצה את זאת; מעדיפה את השמלה האדומה.

But the full sentence with both אני sounds perfectly normal and clear.

No. It is a very normal Hebrew word order.

The basic pattern here is:

• Subject + לא + verb + object

So:

• אני לא רוצה את זאת
• אני מעדיפה את השמלה האדומה

Also note that לא comes before the verb:

• לא רוצה = do not want

Hebrew can change word order for emphasis, but this sentence uses a straightforward, neutral structure.