רוב הזמן אני לא מספרת סודות, אבל אם חברה סומכת עליי, אני שומרת את הסוד שלה.

Because the speaker is female.

In Hebrew present tense, verbs agree with the subject in gender and number.
So:

• אני לא מספרת = I (female) do not tell
• אני שומרת = I (female) keep

If the speaker were male, you would say:

• אני לא מספר סודות
• אני שומר את הסוד שלה

Also notice that סומכת is feminine too, but there it agrees with חברה (a female friend), not with אני.

רוב הזמן means most of the time.

Literally:

• רוב = most / the majority
• הזמן = the time

So the phrase means most of the time or usually.

Hebrew often uses this expression where English might say:

• usually
• most of the time
• generally

Because את marks a definite direct object.

Compare:

• אני לא מספרת סודות = I don’t tell secrets
  Here סודות is indefinite and general, so there is no את.

• אני שומרת את הסוד שלה = I keep her secret
  Here הסוד שלה is definite (her secret, a specific secret), so Hebrew uses את.

A helpful rule:

• definite object → usually use את
• indefinite object → usually no את

The verb לספר means to tell.

So:

• לספר סוד = to tell a secret
• לספר סודות = to tell secrets

This is just the normal Hebrew verb for telling a story, fact, or secret.

Be aware that the same root can also relate to counting in other forms, which can confuse learners:

• לספור = to count
• לספר = to tell

They look similar, but they are different verbs.

סומכת עליי means trusts me or relies on me.

The verb is לסמוך על = to rely on / trust.
So Hebrew uses the preposition על where English just uses a direct object.

Literally, it is something like:

• חברה סומכת עליי = a friend relies on me / trusts in me

The form עליי means on me:

• על = on
• -יי = me

You may also see עלי in writing without the extra yod. עליי makes the pronunciation clearer.

Yes, חברה can mean either:

• female friend
• company

Here it clearly means female friend because of the context:

• אם חברה סומכת עליי = if a friend trusts me

A company would not normally fit this sentence.

Also, if Hebrew wanted to say the company, it would often be החברה, and the surrounding meaning would usually make it obvious.

Because this means if a friend trusts me, not if the friend trusts me.

In Hebrew:

• חברה = a friend / friend in a general sense
• החברה = the friend

The sentence is talking about a general situation, not one specific already-identified friend. That is why the noun is indefinite.

This is very natural in conditional sentences:

• אם חבר מתקשר... = if a friend calls...
• אם ילדה שואלת... = if a girl asks...

Because the sentence moves from a general habit to a specific case.

• אני לא מספרת סודות = a general statement: I don’t tell secrets
• אני שומרת את הסוד שלה = a specific situation: I keep her secret

So the plural in the first part means secrets in general, while the singular in the second part refers to one particular secret belonging to her.

In standard Hebrew, a noun with a possessive like שלי / שלך / שלה is usually treated as definite.

So:

• הסוד שלה = her secret
• הספר שלי = my book
• הבית שלהם = their house

This is why the noun usually takes ה and why it also takes את when it is a direct object:

• אני שומרת את הסוד שלה

In casual speech, people sometimes drop the ה, but the standard form here is הסוד שלה.

Yes, but it would mean something slightly different.

• אני שומרת סוד = I keep a secret / I can keep a secret
  This is more general.

• אני שומרת את הסוד שלה = I keep her secret
  This is specific.

So the sentence you have is talking about a particular secret that belongs to her, not just the general ability to keep secrets.

The sentence is:

רוב הזמן אני לא מספרת סודות, אבל אם חברה סומכת עליי, אני שומרת את הסוד שלה.

A rough breakdown is:

• רוב הזמן = time expression
• אני לא מספרת סודות = main clause
• אבל = but
• אם חברה סומכת עליי = if-clause
• אני שומרת את הסוד שלה = result/main clause

Hebrew word order is fairly flexible, but this order is very natural.
The sentence structure is basically:

Most of the time + I don’t tell secrets, but if a friend trusts me, I keep her secret.

A rough pronunciation guide is:

rov ha-zman ani lo mesaperet sodot, aval im khavera somekhet alai, ani shomeret et ha-sod shela

A few notes:

• רוב הזמן = rov ha-zman
• מספרת = mesaperet
• סודות = sodot
• חברה = khavera or chavera
  The ח is a throaty sound, like the ch in German Bach
• סומכת = somekhet
• עליי = alai
• שומרת = shomeret
• שלה = shela

The stress is usually near the end in words like:

• mesaPEret
• soMEkhet
• shoMEret

Yes. חברה means female friend.

For a male friend, use חבר.

So you could say:

• אם חבר סומך עליי, אני שומרת את הסוד שלו
  = If a male friend trusts me, I keep his secret

Notice how the forms change:

• חברה סומכת = female friend trusts
• חבר סומך = male friend trusts
• הסוד שלה = her secret
• הסוד שלו = his secret

This is an important part of Hebrew: nouns, verbs, and possessives often show gender clearly.