ראיתי אותה לאחרונה.

Because ראיתי is the past tense, first-person singular form of the verb לראות (to see).

• Root: ר-א-ה
• Base meaning: see
• -תי at the end often marks I in the past tense

So:

• ראיתי = I saw

In Hebrew, the subject is often built into the verb, so you do not need a separate word for I here.

Because Hebrew verbs often already show who did the action.

In ראיתי, the ending -תי tells you the subject is I. So:

• ראיתי אותה = I saw her
• אני ראיתי אותה also works, but it sounds more emphatic, like I saw her / I was the one who saw her

In a neutral sentence, leaving out אני is completely normal.

Because אותה is an object pronoun, while היא is a subject pronoun.

• היא = she
• אותה = her

In this sentence, her is receiving the action of seeing, so Hebrew uses the object form:

• ראיתי אותה = I saw her

You would use היא as the subject of a sentence, for example:

• היא ראתה אותי = She saw me

Because with object pronouns like אותי, אותך, אותו, אותה, the idea of את is already built in.

Compare:

• ראיתי את דנה = I saw Dana
• ראיתי אותה = I saw her

So you do not say ראיתי את אותה in this meaning.
Standard Hebrew uses just אותה.

לאחרונה means recently, lately, or in recent times.

In this sentence:

• ראיתי אותה לאחרונה = I saw her recently

It refers to time and works as an adverb.

A learner may confuse it with expressions like:

• אחר כך = afterwards / later
• לאחר מכן = after that

But לאחרונה specifically means recently, not later.

That is a very natural word order in Hebrew.

Hebrew often allows some flexibility, but this order sounds normal:

• ראיתי אותה לאחרונה = I saw her recently

You can also move לאחרונה for emphasis:

• לאחרונה ראיתי אותה = Recently, I saw her

The meaning stays basically the same, but the emphasis shifts slightly.

Yes, sometimes.

Hebrew often uses the simple past where English might use either:

• I saw
• I have seen

So depending on context, ראיתי אותה לאחרונה could be understood as:

• I saw her recently
• I’ve seen her recently

In most everyday translations, I saw her recently is the most direct choice.

Not always. אותה can also mean it, if the thing being referred to is a feminine noun.

For example:

• ראיתי את המכונית. ראיתי אותה אתמול.
  I saw the car. I saw it yesterday.

Because מכונית (car) is feminine, אותה can mean it there.

So in isolation, אותה can mean:

• her
• it (for a feminine noun)

In your sentence, the intended meaning is her.

You would use אותו instead of אותה:

• ראיתי אותו לאחרונה = I saw him recently

So:

• אותו = him / it (masculine)
• אותה = her / it (feminine)

A simple pronunciation guide is:

• ראיתי אותה לאחרונה
  ra-EE-ti o-TA le-a-kha-ro-NA

A few notes:

• ראיתי has the stress on EE
• אותה has the stress on TA
• לאחרונה has the stress on the last syllable: NA
• The ח sound in לאחרונה is the throaty sound heard in Bach or Scottish loch

The structure is:

• ראיתי = verb = I saw
• אותה = direct object = her
• לאחרונה = time expression = recently

So the pattern is:

• Verb + object + time expression

That is a very common and natural Hebrew structure.