Paborito ni Liza ang asul na palda, pero gusto ni Maria ang puting palda na may kaunting berde.

That is a very normal Filipino sentence pattern. Filipino often puts the predicate first.

So:

• Paborito ni Liza ang asul na palda
• Gusto ni Maria ang puting palda na may kaunting berde

are both natural.

In English, we often expect something like Liza's favorite is the blue skirt or Maria likes the white skirt... But in Filipino, it is very common to start with the idea being stated:

• Paborito = favorite
• gusto = liked / wants / prefers, depending on context

Also, Filipino often does not need a word like is in the first clause. So Paborito ni Liza ang asul na palda is complete without any separate verb meaning is.

Because Liza and Maria are not marked as the ang/si-topic in these clauses. After words like paborito and gusto, the person who experiences the feeling or preference is often marked with the genitive marker:

• ni for a singular personal name
• nina for plural personal names

So:

• ni Liza = of Liza / by Liza
• ni Maria = of Maria / by Maria

Using si would mark the name as the main topic of the clause, which is not what is happening here.

You can compare:

• Gusto ni Maria ang palda. = Maria likes the skirt.
• Si Maria ang may gusto sa palda. = Maria is the one who likes the skirt.

Both are possible, but they are structured differently.

Ang marks the topic/focus noun phrase of the clause.

Here, it marks the things being talked about:

• ang asul na palda
• ang puting palda na may kaunting berde

So in the first clause, the topic is the blue skirt.
In the second clause, the topic is the white skirt with a little green.

A helpful way to think of it is:

• ni Liza / ni Maria = whose preference or liking it is
• ang ... palda = the thing that is favorite or liked

This is because Filipino uses a linker to connect modifiers and the words they describe. The linker has two common forms:

• na
• -ng

Which form you use depends on the sound at the end of the word before it.

In your sentence:

• asul na palda
  asul ends in a consonant, so the separate linker na is used.

• puting palda
  puti ends in a vowel, so -ng is attached, giving puting.

• kaunting berde
  kaunti also ends in a vowel, so it becomes kaunting.

So na and -ng are doing the same job here: they connect a describing word to the word that follows.

Here, na links palda to a longer descriptive phrase:

• palda na may kaunting berde

This works a lot like English that has or with.

So the phrase means something like:

• a skirt that has a little green
• a skirt with a little green

This is still the same general linker idea, but now it is connecting a noun (palda) to a descriptive phrase (may kaunting berde), not just to a single adjective.

May here means has or with, depending on how you translate it in English.

So:

• may kaunting berde = has a little green / with a little green

In Filipino, may is commonly used to show existence or possession.

Examples:

• may pera = has money / there is money
• may oras = has time / there is time
• palda na may berde = skirt with green

You may also learn mayroon, which is a fuller form. In many cases, may is the more natural choice before a noun phrase.

Kaunting berde literally means a little green or a small amount of green.

• kaunti = little / few / a small amount
• kaunting = kaunti
  • linker
• berde = green

In this phrase, berde behaves more like a thing/substance/color than like a simple adjective. In English we also do this sometimes:

• a little green
• some red
• a bit of blue

So although berde is usually a color word used adjectivally, here it functions more like green color or green detail.

They are related, but they are not exactly the same.

• paborito = favorite
• gusto = like / want

So:

• Paborito ni Liza ang asul na palda means the blue skirt is Liza’s favorite
• Gusto ni Maria ang puting palda... means Maria likes the white skirt...

That means Liza’s preference sounds stronger or more specific: it is her favorite, not just something she likes.

A learner should notice that the two clauses are not perfectly parallel in meaning:

• paborito = top choice / favorite
• gusto = likes / prefers / wants, depending on context

Yes, at least the first clause can very naturally be rewritten with ay:

• Ang asul na palda ay paborito ni Liza.

This puts the ang-phrase first, which can feel a little more like English structure.

The second clause can also be rephrased, though Gusto ni Maria ang puting palda na may kaunting berde is already very natural. A possible alternative is:

• Ang puting palda na may kaunting berde ang gusto ni Maria.

This version gives extra emphasis to the white skirt with a little green.

So:

• predicate first = very common, neutral
• ang ... ay ... = also correct, sometimes more formal or more deliberate in tone

Yes. Pero is a very common everyday word for but in Filipino.

So:

• ..., pero ... = ..., but ...

It is extremely natural in speech and writing.

You may also see:

• ngunit = but, more formal
• subalit = but, also more formal/literary

In this sentence, pero is the most natural conversational choice.

Yes. The same basic pattern stays the same, but ni + name changes to the appropriate genitive pronoun.

For example:

• Paborito ko ang asul na palda. = The blue skirt is my favorite.
• Gusto niya ang puting palda. = She likes the white skirt.
• Paborito namin ang asul na palda. = The blue skirt is our favorite.

This is another clue that ni Liza and ni Maria are in the genitive role, not the siya/ako type of role.

So:

• ni Liza matches pronoun patterns like ko, mo, niya, namin, nila
• not the ako, ikaw, siya set

That is why ni is the right marker in your sentence.