Me dedico a mi familia.

Because dedicarse a is a very common pronominal verb pattern in Spanish.
Here, me matches the subject yo and is part of the expression dedicarse a.

So:

• me dedico = I devote myself / I am engaged in
• te dedicas = you devote yourself / you are engaged in
• se dedica = he/she devotes himself/herself / is engaged in

In this sentence, me does not need to be translated word-for-word as myself every time. It is simply how this verb is normally used in this meaning.

Because the expression is dedicarse a + noun / activity / person.

So the pattern is:

• Me dedico a mi familia
• Se dedica a la música
• Nos dedicamos a la enseñanza

That a belongs to the verb pattern. It is not optional here.

Not really. In this sentence, the a is mainly there because dedicarse requires it.

So in Me dedico a mi familia, think of a as part of the structure dedicarse a.

Even though familia refers to people, the key reason the a appears is the verb pattern, not the usual personal-a rule.

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

• mi familia = my family

mí with an accent is a pronoun used after prepositions:

• para mí = for me
• a mí = to me

Since mi is directly modifying the noun familia, it has no accent.

Yes. That is completely correct.

Spanish often leaves out subject pronouns when they are clear from the verb:

• Me dedico a mi familia
• Yo me dedico a mi familia

Both are correct.
Adding yo usually gives emphasis, contrast, or a more explicit tone.

For example:

• Yo me dedico a mi familia; él se dedica al trabajo.

It is the present tense, first person singular, from dedicar.

Conjugation:

• yo dedico
• tú dedicas
• él/ella se dedica when using the pronominal form
• nosotros nos dedicamos

So me dedico means I devote myself / I am dedicated / I am engaged, depending on context.

This is a very important question.

dedicar

Usually means to dedicate something to someone/something.

Examples:

• Dedico mucho tiempo a mi familia.
  = I dedicate a lot of time to my family.
• Le dedicó una canción.
  = He/She dedicated a song to him/her.

dedicarse a

Usually means to devote oneself to or to be engaged in / to work in.

Examples:

• Me dedico a mi familia.
  = I devote myself to my family.
• Se dedica a la medicina.
  = He/She works in medicine.
• ¿A qué te dedicas?
  = What do you do? / What do you do for a living?

So the me changes the structure and often the meaning.

Yes, very often.

In everyday Spanish, dedicarse a is commonly used to talk about what someone does professionally:

• Me dedico a la enseñanza.
• Se dedica a la informática.
• ¿A qué te dedicas?

But with mi familia, it usually means someone is devoting their time and attention to their family, not naming a formal profession.

So this structure can express either:

• occupation / field
• personal dedication / life focus

Context tells you which one is meant.

Because Spanish normally uses a possessive adjective like mi instead of an article in this kind of phrase.

So you say:

• mi familia
• mi casa
• mi trabajo

Not:

• la mi familia in standard modern Spanish

The possessive already does the job.

Yes, it is natural. It sounds like the speaker is saying that their time, effort, or life focus is centered on their family.

It often suggests something stronger than simply I spend time with my family. It can imply:

• commitment
• responsibility
• life focus
• personal priority

Depending on context, it may sound like:

• I devote myself to my family
• I focus on my family
• My family is what I give my time to

So it is a meaningful, fairly strong statement.

The normal word order is:

• Me dedico a mi familia.

You can add emphasis in other ways, but this standard order is the most natural.

For example:

• Yo me dedico a mi familia.
  adds emphasis to yo
• A mi familia me dedico
  is grammatically possible in a very marked or poetic context, but it is not the normal everyday order

For a learner, the safest and most natural version is the original one.

Yes, but it is not exactly the same.

• Me dedico a mi familia focuses on what you devote yourself to as an ongoing activity or life focus.
• Estoy dedicado/a a mi familia describes a state of being dedicated.

Also, dedicado/a changes for gender:

• Estoy dedicado a mi familia.
• Estoy dedicada a mi familia.

Both are possible, but me dedico a is especially common when talking about what someone actively gives their time or life to.