El éxito de mi hermana me hace feliz.

Because éxito is a masculine noun in Spanish, so it takes el.

A few useful points:

• éxito = success
• It ends in -o, which is often a sign that a noun is masculine
• So: el éxito

Examples:

• el éxito
• un éxito
• mucho éxito

De mi hermana means of my sister or, more naturally in English, my sister’s.

So:

• el éxito de mi hermana = my sister’s success

Spanish often uses de where English uses ’s.

Compare:

• el coche de mi padre = my father’s car
• la casa de Ana = Ana’s house
• el éxito de mi hermana = my sister’s success

Me means to me and shows who is affected.

In this sentence:

• El éxito de mi hermana = the thing causing the feeling
• me = the person experiencing the result
• hace feliz = makes happy

So the structure is basically:

• [Something] + me + hace + [adjective]
• [Something] makes me [adjective]

Other examples:

• Me hace reír = It makes me laugh
• Me hace pensar = It makes me think
• Me hace feliz = It makes me happy

Because the subject is el éxito, which is singular.

The full subject is:

• El éxito de mi hermana

The main noun there is éxito, not hermana.
De mi hermana is just extra information telling you whose success it is.

So:

• El éxito ... me hace feliz = singular subject → hace

If the subject were plural, then the verb would be plural too:

• Los éxitos de mi hermana me hacen feliz = My sister’s successes make me happy

Here hacer means to make in the sense of causing a state or feeling.

So:

• hacer feliz = to make happy

This is a very common Spanish pattern:

• hacer + adjective
• hacer + infinitive

Examples:

• Me hace feliz = It makes me happy
• Me hace triste = It makes me sad
• Me hace pensar = It makes me think
• Me hace reír = It makes me laugh

So hacer here does not mean to do. It means to make/cause.

Because Spanish does not need one in this structure.

In English, we say:

• It makes me happy

Not:

• It makes me to happy

Spanish works the same way here:

• me hace feliz

Feliz is simply the adjective describing the result.

Yes, absolutely. That is a natural sentence too.

There is a small difference in focus:

• El éxito de mi hermana me hace feliz
  = My sister’s success makes me happy
  Focus: the cause

• Estoy feliz por el éxito de mi hermana
  = I’m happy about my sister’s success
  Focus: your emotional state

Both are correct, but the original sentence emphasizes what is causing the feeling.

Because de shows possession/relationship here.

• de mi hermana = of my sister / my sister’s

You would use a for other functions, such as marking a person who is a direct or indirect object, but not for possession.

Compare:

• El éxito de mi hermana = My sister’s success
• Veo a mi hermana = I see my sister

So in your sentence, mi hermana is not the object of the verb hacer. She is part of the noun phrase el éxito de mi hermana.

Yes. The most neutral order is:

• El éxito de mi hermana me hace feliz.

But Spanish can also say:

• Me hace feliz el éxito de mi hermana.

This still means the same thing. It may sound a bit more literary or place slightly more focus on the result me hace feliz before naming the cause.

In both versions:

• me stays before the conjugated verb hace

Because feliz is one of those adjectives that has the same form for masculine and feminine.

So you get:

• feliz for a man
• feliz for a woman

Examples:

• Estoy feliz
• Ella está feliz
• Mi hermano está feliz
• Mi hermana está feliz

It does change in the plural:

• felices

Examples:

• Ellos están felices
• Mis padres están felices

Yes, but the meaning changes.

• mi hermana = my sister
• su hermana = his/her/your(formal)/their sister

So:

• El éxito de mi hermana me hace feliz = My sister’s success makes me happy
• El éxito de su hermana me hace feliz = His/Her/Your/Their sister’s success makes me happy

For a learner, su can be ambiguous, so de mi hermana is very clear.

Yes. Éxito is the normal and very common word for success.

Examples:

• Tuvo mucho éxito = He/She was very successful / It was very successful
• El éxito del proyecto = The success of the project
• Es un gran éxito = It is a great success

So in this sentence, éxito is exactly the word you would expect.

A useful breakdown is:

• El éxito de mi hermana = subject
• me = indirect object pronoun-like element showing who is affected
• hace = verb
• feliz = adjective showing the result/state

So the pattern is:

• [Subject] + me/te/le/nos/os/les + hace + [adjective]

Examples:

• Tu apoyo me hace fuerte = Your support makes me strong
• Esta música me hace feliz = This music makes me happy
• La noticia nos hace optimistas = The news makes us optimistic

This is a very useful pattern to learn because it appears often in everyday Spanish.