ההגייה שלה נשמעת טבעית.

Word by word:

• ההגייה = the pronunciation
• שלה = her
• נשמעת = sounds / is heard as
• טבעית = natural (feminine singular)

So the whole sentence means Her pronunciation sounds natural.

A simple pronunciation guide is:

ha-ha-gi-YA she-LA nish-MA-at tiv-IT

A few notes:

• ההגייה has two written ה letters because the noun itself begins with ה, and it also has the definite article ה־.
• שלה is pronounced she-LA.
• טבעית is pronounced roughly tiv-IT.

Because the base word is הגייה = pronunciation, and when you add the definite article ה־ = the, you get:

• הגייה = pronunciation
• ההגייה = the pronunciation

So the first ה is the, and the second ה is part of the noun itself.

In Hebrew, possession with של often still uses the definite article on the noun when the meaning is definite.

So:

• ההגייה שלה = her pronunciation
• literally, something like the pronunciation of hers

This is normal Hebrew structure.
English does not say the pronunciation her, but Hebrew often uses:

• ה + noun + של/שלה/שלו...

So ההגייה שלה is exactly what you expect for her pronunciation.

שלה means hers or her depending on context.

In this sentence, it means her:

• ההגייה שלה = her pronunciation

Related forms are:

• שלו = his
• שלה = her
• שלהם = their
• שלי = my
• שלך = your

So שלה tells you who the pronunciation belongs to.

Because the subject is ההגייה, and הגייה is a feminine noun.

In Hebrew, present-tense verbs agree with the subject in gender and number. Since ההגייה is feminine singular, the verb must also be feminine singular:

• masculine singular: נשמע
• feminine singular: נשמעת

So here we need נשמעת.

Because adjectives also agree with the noun they describe.

Since ההגייה is feminine singular, the adjective must be feminine singular too:

• טבעי = natural (masculine singular)
• טבעית = natural (feminine singular)

So:

• ההגייה שלה נשמעת טבעית = correct
• ההגייה שלה נשמעת טבעי = incorrect

Yes. נשמעת comes from the verb להישמע, which literally has the sense of to be heard or to sound.

In natural English, you usually translate it here as sounds:

• ההגייה שלה נשמעת טבעית = Her pronunciation sounds natural

A more literal sense would be something like:

• Her pronunciation is heard as natural

But that sounds awkward in English, so sounds natural is the best translation.

Yes, you can, but the meaning shifts slightly.

• ההגייה שלה טבעית = Her pronunciation is natural
• ההגייה שלה נשמעת טבעית = Her pronunciation sounds natural

The version with נשמעת focuses on how it comes across to the listener.
The version without it is a more direct statement.

Both are good Hebrew; they just are not exactly identical in nuance.

Yes. A more compact, more formal, or more written-style version is:

• הגייתה נשמעת טבעית

Here, הגייתה means her pronunciation all in one word.

Compare:

• ההגייה שלה = more common and transparent for learners
• הגייתה = more compact, somewhat more formal/literary

Both are correct.

Only the possessive word changes. The verb and adjective stay feminine singular because הגייה is still feminine singular.

• ההגייה שלו נשמעת טבעית = His pronunciation sounds natural
• ההגייה שלה נשמעת טבעית = Her pronunciation sounds natural
• ההגייה שלהם נשמעת טבעית = Their pronunciation sounds natural

That is an important point:
the agreement is with ההגייה, not with the person who owns it.