Mi hermana siempre estudia a su manera.

Because mi without an accent is the possessive adjective meaning my.

• mi hermana = my sister
• mí with an accent is a pronoun used after prepositions:
  • para mí = for me
  • sin mí = without me

So in this sentence, you need mi because it comes directly before a noun.

In standard modern Spanish, a possessive like mi, tu, su, nuestro, etc. usually replaces the article.

So you say:

• mi hermana = my sister
• not la mi hermana

This is especially normal with family members and everyday nouns.

Estudia is the third-person singular present indicative of estudiar.

The verb pattern is:

• yo estudio
• tú estudias
• él / ella / usted estudia
• nosotros estudiamos
• vosotros estudiáis
• ellos / ellas / ustedes estudian

Since the subject is mi hermana (my sister), the verb has to be estudia.

Grammatically, Spanish present tense can sometimes cover both ideas depending on context.

But in this sentence, because of siempre (always), the meaning is clearly habitual:

• Mi hermana siempre estudia... = My sister always studies...

So here it means studies, not is studying right now.

If you wanted to stress that she is studying at this moment, Spanish would often use:

• Mi hermana está estudiando.

That is the most neutral and common position here.

• Mi hermana siempre estudia a su manera.

In Spanish, adverbs like siempre, nunca, a menudo, and ya often go before the conjugated verb.

You can move siempre in some cases, but the emphasis changes a little:

• Mi hermana estudia siempre a su manera.
  Also possible, but a bit less neutral.
• Siempre mi hermana estudia a su manera.
  Much less natural in normal conversation unless you are emphasizing something.

So the original word order is very natural.

A su manera is a very common expression meaning:

• in her own way
• in her own style
• according to her own method

It often suggests that someone does things the way they personally prefer, not necessarily the standard way.

Depending on context, it can sound:

• neutral: she has her own method
• positive: she is independent
• slightly critical: she does things her own way and does not follow others

Because a su manera is a fixed Spanish expression.

You should think of it as a chunk:

• a mi manera = in my own way
• a tu manera = in your own way
• a su manera = in his/her/their own way

The a here is not the personal a used before people as direct objects. It is simply part of the expression.

English uses in here, but Spanish uses a. That is just one of those preposition differences you have to learn as a phrase.

Because before a noun, Spanish uses the short possessive adjective:

• mi manera
• tu manera
• su manera

Forms like mío, tuyo, suyo, suya are different and are usually used:

1. After a noun in certain structures:
   • una amiga suya = a friend of his/hers
2. On their own as pronouns:
   • La manera es suya. = The method/way is hers.

So directly before manera, the correct form is su.

In this sentence, su is most naturally understood as her, because the subject is mi hermana.

However, grammatically su can mean:

• his
• her
• your (formal singular)
• their
• your (formal plural, in some contexts)

So yes, su is potentially ambiguous in Spanish. Context usually makes it clear.

If you really wanted to make it explicit, you could say:

• Mi hermana siempre estudia a la manera de ella.
  This is possible, but less natural here.
• or more naturally just keep a su manera, because the context already points to her.

It could be, but a su manera already often implies her own way.

• a su manera = natural and common
• a su propia manera = more emphatic, stressing that it is specifically her own way

So the sentence without propia sounds smoother and more idiomatic in everyday Spanish.

Yes, Spanish word order is somewhat flexible, but different versions sound more or less natural and may shift the emphasis.

Examples:

• Mi hermana siempre estudia a su manera.
  Most neutral.
• Mi hermana estudia siempre a su manera.
  Also possible.
• A su manera, mi hermana siempre estudia.
  Possible, but now a su manera is strongly emphasized.

For a learner, the original order is the safest and most natural choice.

Yes. This is a very useful pattern.

• a mi manera = in my own way
• a tu manera = in your own way
• a nuestra manera = in our own way
• a vuestra manera = in your own way (Spain, plural)
• a su manera = in his/her/their own way

So once you learn a su manera, you can reuse the structure very easily.

Yes, it sounds completely natural in Spain.

A speaker from Spain would understand it immediately as a normal sentence meaning that your sister studies in her own way or using her own method.

Nothing in it sounds odd or overly formal. It is a good, standard example of everyday Spanish.