היא גאה בי, ולכן היא מחייכת.

Because the subject is היא (she), and adjectives in Hebrew agree with the person they describe.

• masculine singular: גאה
• feminine singular: גאה
• masculine plural: גאים
• feminine plural: גאות

In this particular adjective, the masculine and feminine singular happen to look the same in writing, so you do not see a spelling change here. The feminine agreement is understood from the subject היא.

The adjective גאה commonly takes the preposition ב־ when you say who someone is proud of.

So:

• אני גאה בך = I am proud of you
• היא גאה בי = she is proud of me

Even though English uses of, Hebrew uses ב־ here. This is something you mainly have to learn as part of the expression להיות גאה ב־.

בי is the preposition ב־ (in / with / at / of, depending on context) plus the pronoun ending for me.

So:

• ב + י = בי
• בי = in me / with me / of me, depending on the expression

In this sentence, because of the adjective גאה, בי means of me.

Some related forms are:

• בך = in you / of you
• בו = in him / of him
• בה = in her / of her
• בנו = in us / of us

In present-tense Hebrew, you usually do not use a word for is / am / are in simple sentences like this.

So:

• היא גאה בי = she is proud of me
• literally: she proud of me

This is completely normal in Hebrew. In past and future, Hebrew does use forms of to be when needed, but in the present tense they are usually omitted.

ולכן means and therefore / and so / therefore.

It is made of:

• ו־ = and
• לכן = therefore / so

Hebrew often attaches short function words directly to the following word, especially ו־ (and), ב־, ל־, and כ־.

So ולכן is simply ו + לכן written as one word.

Hebrew often repeats the subject after a connector like ולכן, especially when starting a new clause.

So:

• היא גאה בי, ולכן היא מחייכת.

sounds natural and clear.

You may also hear sentences where the subject is omitted if it is already obvious from the verb and context, but repeating היא is very normal. It makes the sentence clearer and a little more explicit.

Because it agrees with היא.

In the present tense, many Hebrew verbs behave like adjectives in agreement:

• מחייך = smiling, masculine singular
• מחייכת = smiling, feminine singular
• מחייכים = masculine plural
• מחייכות = feminine plural

Since the subject is she, the correct form is מחייכת.

In this sentence, it functions as the present-tense verb: she is smiling.

But grammatically, Hebrew present-tense verb forms often look like participles and behave in adjective-like ways, especially because they change for gender and number.

So for a learner, it is helpful to think:

• function in the sentence: verb
• form: participle-like, with gender/number agreement

That is why מחייכת changes form depending on who is doing the action.

A simple pronunciation guide is:

Hi ge'ah bi, ve-lakhen hi mekhayekhet.

A few notes:

• היא = hi
• גאה is often pronounced roughly ge'ah, with a break between the two vowels
• בי = bi
• ולכן = ve-lakhen
• מחייכת = mekhayekhet or mechayekhet, depending on how you represent ח

The letter ח is the throaty sound that English does not really have.

Sometimes yes, but not every change sounds equally natural.

The original sentence:

• היא גאה בי, ולכן היא מחייכת.

is very natural.

You could also say:

• היא גאה בי ולכן היא מחייכת.

without the comma in less formal writing.

You might also hear:

• היא גאה בי, ולכן מחייכת.

if the subject in the second clause is understood, but this is a little less explicit.

For learners, the full version with both היא words is the safest and clearest.

In careful writing, a comma before ולכן is common because it introduces a result clause: therefore / so.

So:

• היא גאה בי, ולכן היא מחייכת.

looks perfectly natural.

In casual writing, people may leave the comma out, but the meaning does not change.

Yes. לכן by itself also means therefore / so.

For example:

• היא גאה בי; לכן היא מחייכת.

That is more formal in style. In everyday Hebrew, ולכן is very common because it flows naturally as and therefore / and so.

Yes. Both parts are present-time statements.

• היא גאה בי = she is proud of me
• היא מחייכת = she is smiling

Hebrew does not need a separate present-tense is in the first clause, and in the second clause the present tense is shown by the form מחייכת itself.