Моя мати виглядає дуже молодо.

Because мати is a feminine singular noun in the nominative case, and the possessive pronoun my has to agree with it.

So:

• мій = my, for masculine nouns
• моя = my, for feminine nouns
• моє = my, for neuter nouns
• мої = my, for plural nouns

Since мати is feminine, you say моя мати.

Compare:

• мій брат = my brother
• моя сестра = my sister
• моє місто = my city
• мої друзі = my friends

It is in the nominative case because it is the subject of the sentence — the person doing the action of виглядає.

In Моя мати виглядає дуже молодо, the subject is моя мати = my mother.

So the basic structure is:

• Моя мати = subject
• виглядає = verb
• дуже молодо = description of how she looks

Yes — мама is usually more common in everyday speech.

The difference is roughly:

• мати = mother, more formal, neutral, or literary
• мама = mom, more natural in ordinary conversation

So this sentence is correct, but it sounds a bit more formal or written than:

• Моя мама виглядає дуже молодо.

A learner should know both words:

• мати is very useful in textbooks, writing, and formal contexts
• мама is what you will often hear in real life

Виглядає is the 3rd person singular present tense form of виглядати.

Base form:

• виглядати = to look, to appear

In this sentence, виглядає means looks / appears.

Conjugation in the present tense:

• я виглядаю = I look
• ти виглядаєш = you look
• він / вона / воно виглядає = he / she / it looks
• ми виглядаємо = we look
• ви виглядаєте = you look
• вони виглядають = they look

Since мати is she, you use виглядає.

This is one of the most important things to notice in the sentence.

• молода is an adjective meaning young in feminine singular
• молодо is an adverb, meaning something like youngly / in a young way, but in natural English we translate it simply as young

After the verb виглядати meaning to look / appear, Ukrainian often uses an adverb to describe appearance:

• виглядати добре = to look good / well
• виглядати погано = to look bad
• виглядати дивно = to look strange
• виглядати молодо = to look young

But if you are simply saying she is young, you use the adjective:

• Моя мати молода. = My mother is young.

So:

• Моя мати молода. = she is young
• Моя мати виглядає молодо. = she looks young

That difference is very important.

Дуже means very. It intensifies молодо:

• молодо = young
• дуже молодо = very young

Дуже is an adverb, and it does not change for gender, number, or case.

So you can use it the same way in many sentences:

• дуже добре = very well
• дуже гарний = very beautiful / handsome / nice
• дуже швидко = very quickly

In your sentence, it simply strengthens the idea: she does not just look young — she looks very young.

Ukrainian word order is more flexible than English, but the neutral, most straightforward order here is:

• Моя мати виглядає дуже молодо.

You can move things around for emphasis, but the meaning stays similar. For example:

• Моя мати дуже молодо виглядає.
• Дуже молодо виглядає моя мати.

These are possible, but they sound more marked or emphatic. A learner should usually stick to the neutral order unless there is a special reason to emphasize something.

So the sentence as given is the safest and most natural basic pattern.

Sometimes yes, but it changes the feel.

• Моя мати виглядає дуже молодо. = My mother looks very young.
• Мати виглядає дуже молодо. = Mother looks very young.

Without моя, it can sound more formal, literary, or dependent on context. In everyday speech, if you mean my mom, people often say:

• Моя мама виглядає дуже молодо.

So grammatically, omitting моя can be possible in some contexts, but for a learner, keeping моя is clearer and more natural unless the relationship is already obvious.

A simple pronunciation guide is:

• моя → mo-YA
• мати → MA-ty
• виглядає → vyh-lya-DA-ye
• дуже → DU-zhe
• молодо → MO-lo-do

Stress:

• моя́
• ма́ти
• вигляда́є
• ду́же
• мо́лодо

One useful note: Ukrainian г is usually pronounced more like a soft h sound than a hard English g. So виглядає is closer to vyhlya-DA-ye than viglya-DA-ye.

Not in this meaning.

In modern Ukrainian, the verb to be in the present tense is usually not expressed in simple sentences like:

• Моя мати молода. = My mother is young.

Also, your original sentence uses виглядати = to look / appear, not to be.

So these are different:

• Моя мати молода. = My mother is young.
• Моя мати виглядає дуже молодо. = My mother looks very young.

As for є, it is not normally used the way English uses is in ordinary present-tense descriptions.

Ukrainian makes the same distinction as English, but the grammar is different.

1. She is young

   • Моя мати молода.
   • adjective: молода

2. She looks young

   • Моя мати виглядає молодо.
   • adverb: молодо

So if you want to describe her actual age category or state, use the adjective:

• молода

If you want to describe her appearance, use виглядає + adverb:

• виглядає молодо

That is why the sentence uses молодо, not молода.