אני גרה בקומה השלישית.

Because גרה is the feminine singular form of the verb/adjective-like participle גר / גרה meaning live / reside.

So:

• אני גר = I live said by a male
• אני גרה = I live said by a female

Hebrew often shows the speaker’s gender in the verb form, even when English does not.

Yes, אני is optional in many contexts.

Hebrew verb forms often already give enough information, so:

• אני גרה בקומה השלישית = full, explicit
• גרה בקומה השלישית = natural if the subject is already clear from context

Including אני can make the sentence clearer, more neutral, or slightly more emphatic.

Because the preposition ב־ (in / on / at) is attached directly to the noun.

The full underlying form is:

• ב + ה + קומה = בקומה

This is a common Hebrew contraction:

• ב + ה... often becomes בַּ... in fully pointed Hebrew

So בקומה השלישית means on the third floor / in the third-floor level.

Even though you do not separately see ה before קומה in the unpointed spelling, the phrase is still definite because of the contracted article.

Because it means the third, not just third.

Hebrew adjectives and ordinal numbers usually match the noun in:

• gender
• number
• definiteness

Here:

• קומה = a feminine singular noun
• השלישית = feminine singular definite form of third

So:

• קומה שלישית = a third floor
• הקומה השלישית / בקומה השלישית = the third floor

Because קומה is a feminine noun, and ordinal numbers in Hebrew must agree with the noun.

Compare:

• החדר השלישי = the third room
  (חדר is masculine)
• הקומה השלישית = the third floor
  (קומה is feminine)

So שלישי is masculine, and שלישית is feminine.

Yes. This is one of those places where Hebrew and English use prepositions differently.

In Hebrew, with floors of a building, ב is natural:

• אני גרה בקומה השלישית = literally something like I live in the third floor level
• idiomatic English: I live on the third floor

So although ב often means in, here English usually translates it as on.

Normally, no.

For location in a building floor, Hebrew uses ב:

• בקומה הראשונה
• בקומה השנייה
• בקומה השלישית

Using על here would sound unnatural in standard Hebrew. English says on the third floor, but Hebrew says בקומה השלישית.

קומה means floor or story of a building.

Examples:

• קומה ראשונה = first floor
• קומה שנייה = second floor
• קומה שלישית = third floor

Be aware that English itself can vary by region:

• American English: third floor
• British English may count floors differently in some contexts

But the Hebrew phrase simply refers to the building level.

Because in Hebrew, adjectives usually come after the noun.

So the normal order is:

• noun + adjective

Examples:

• בית גדול = big house
• ילדה חכמה = smart girl
• קומה שלישית = third floor

That is why השלישית comes after קומה.

Yes, it behaves like a regular present-tense form built from the root ג־ו/י־ר meaning to live / reside.

Present tense forms are:

• גר = masculine singular
• גרה = feminine singular
• גרים = masculine plural / mixed plural
• גרות = feminine plural

So:

• אני גר = I live (male speaker)
• אני גרה = I live (female speaker)
• הם גרים = they live
• הן גרות = they live

Usually גר / גרה suggests live in the sense of residence, not just temporarily staying somewhere.

So אני גרה בקומה השלישית normally means the person’s home is on the third floor.

If you wanted to emphasize temporary stay, Hebrew would more likely use another expression, depending on context.

A male speaker would say:

אני גר בקומה השלישית.

The only change is:

• גרה → גר

Everything else stays the same.

A common pronunciation would be:

Ani gara be-koma ha-shlishit.

Roughly:

• אני = ah-NEE
• גרה = ga-RA
• בקומה = be-KO-ma
• השלישית = ha-shli-SHEET

The stress is usually near the end in גרה and on the last syllable in השלישית.