Seguramente mi hermana aprobará el examen porque ha estudiado mucho.

Here seguramente most naturally means probably.

So the sentence is expressing a prediction or strong expectation, not absolute certainty. In English, surely can sound a bit different, and probably is usually the best match in this context.

• Seguramente = probably / very likely
• It suggests the speaker feels fairly confident

In everyday Spanish, this is a very common way to say that something is likely to happen.

Aprobará is the simple future of aprobar.

• aprobar = to pass
• aprobará = he/she will pass

In this sentence, the future is being used for a prediction:

• Seguramente mi hermana aprobará el examen = My sister will probably pass the exam

Spanish often uses the future like this when talking about what the speaker thinks will happen.

Yes. You could say:

• Seguramente mi hermana va a aprobar el examen

This also means My sister is probably going to pass the exam.

The difference is small:

• aprobará sounds a bit more neutral, written, or predictive
• va a aprobar can sound a bit more conversational and immediate

In normal speech, both are perfectly natural.

No. This is an important false friend.

Aprobar can mean:

• to approve
• to pass an exam, test, subject, etc.

In this sentence, aprobar el examen means to pass the exam, not to approve the exam.

Examples:

• El profesor aprobó el plan. = The teacher approved the plan.
• La estudiante aprobó el examen. = The student passed the exam.

El examen means the exam, so it refers to a specific exam that both speaker and listener already know about.

That is very natural if, for example, everyone knows which exam the sister is taking.

• aprobará el examen = she will pass the exam
• aprobará un examen = she will pass an exam

The sentence uses el because this is a particular, known exam.

Ha estudiado is the present perfect:

• ha estudiado = she has studied

In Spanish from Spain, the present perfect is very commonly used for a past action that is seen as connected to the present.

Here, the idea is:

• she has studied a lot
• that studying is relevant now
• therefore she will probably pass

In many parts of Latin America, people might more naturally say estudió mucho in similar situations. But in Spain, ha estudiado mucho is especially natural.

Yes, it would be grammatically correct:

• Seguramente mi hermana aprobará el examen porque estudió mucho.

This means roughly the same thing, but the nuance is a little different.

• ha estudiado mucho highlights a connection to the present: her studying matters now
• estudió mucho sounds more like a finished past event

In Spain, ha estudiado mucho is often the more natural choice when the study period is recent or still relevant.

Because porque here introduces a real cause that the speaker presents as a fact:

• She will probably pass because she has studied a lot

That reason is treated as true, so the indicative is used:

• ha estudiado

After porque, Spanish normally uses the indicative when giving a real explanation or cause.

Here mucho works like an adverb and means a lot.

• ha estudiado mucho = she has studied a lot

It modifies the verb phrase, telling us the degree or amount of studying.

Compare:

• estudia mucho = she studies a lot
• come mucho = she eats a lot
• trabaja mucho = she works a lot

Because in Spanish, words like mucho often come after the verb when they mean a lot.

So:

• ha estudiado mucho = has studied a lot

This is the normal order in Spanish. English learners sometimes expect something closer to much studied, but Spanish does not work that way here.

Yes. Seguramente is quite flexible.

All of these are possible:

• Seguramente mi hermana aprobará el examen...
• Mi hermana seguramente aprobará el examen...
• Mi hermana aprobará seguramente el examen... (less common in everyday speech, but possible)

Putting seguramente at the beginning is very natural because it frames the whole statement as a probability from the start.

Because Spanish often omits subject pronouns when the subject is already clear.

Here the subject is explicitly stated as mi hermana, so there is no need to add ella.

• Mi hermana aprobará el examen = My sister will pass the exam

Adding ella is possible, but usually unnecessary unless you want contrast or emphasis:

• Ella aprobará el examen, no yo. = She will pass the exam, not me.

Because mi meaning my does not take an accent.

Compare:

• mi hermana = my sister
• mí = me / myself, used after prepositions

Examples:

• mi libro = my book
• para mí = for me

So in this sentence, mi hermana is correct because it means my sister.

The stress is on the last syllable:

• a-pro-ba-RÁ

The written accent on á shows that stress.

This matters because Spanish verb endings can change meaning:

• aprueba = he/she passes
• aprobó = he/she passed
• aprobará = he/she will pass

So the accent helps show both pronunciation and grammar.

Because in Spanish, a short adverb like seguramente at the beginning of a sentence does not usually need a comma.

So this is normal:

• Seguramente mi hermana aprobará el examen...

A comma is not impossible in some stylistic contexts, but the version without a comma is the standard, natural one here.

Yes, especially because of ha estudiado mucho.

In Spain, speakers commonly use the present perfect for recent or still-relevant past actions:

• ha estudiado mucho

In many Latin American varieties, speakers might often prefer:

• estudió mucho

Both are correct Spanish, but the original sentence sounds very natural for Spain.