Tu opinión me importa mucho.

Because tu without an accent is a possessive adjective: your.

• tu opinión = your opinion

Tú with an accent is the subject pronoun meaning you.

• Tú hablas = You speak

So in this sentence, tu is correct because it is describing opinión.

Because Spanish stress rules would normally make a word ending in -n stressed on the second-to-last syllable. But opinión is stressed on the last syllable: o-pi-nión.

The written accent shows that irregular stress.

It also helps you pronounce it correctly:

• o-pi-NYON

Because importar works like gustar.

In this structure:

• the thing that matters is the grammatical subject
• the person it matters to is shown with an indirect object pronoun

So in:

• Tu opinión me importa mucho

the parts are:

• tu opinión = the thing that matters
• me = to me
• importa = matters

A very literal breakdown is:

• Your opinion matters to me a lot

That is why me is used, not mi.

• me = to me / me
• mi = my

Because the subject is tu opinión, which is singular.

• Tu opinión me importa mucho = Your opinion matters to me a lot
• Tus opiniones me importan mucho = Your opinions matter to me a lot

The verb agrees with the thing that matters, not with me.

Me is the indirect object pronoun meaning to me.

It tells you who is affected by the verb importar.

So:

• me importa = it matters to me
• te importa = it matters to you
• le importa = it matters to him/her/you (formal)

This is one of the most important patterns to get used to in Spanish, because it is very common with verbs like:

• gustar
• interesar
• molestar
• importar

Here mucho means a lot or very much.

It is working as an adverb, modifying importa:

• me importa mucho = it matters to me a lot / very much

It does not mean many here.

Compare:

• Tengo mucho trabajo = I have a lot of work
  Here mucho is an adjective.

• Te quiero mucho = I love you very much / a lot
  Here mucho is an adverb.

Yes, absolutely. That version is very natural too.

Both are correct:

• Tu opinión me importa mucho
• Me importa mucho tu opinión

The difference is mostly about focus or emphasis:

• Tu opinión me importa mucho puts your opinion first
• Me importa mucho tu opinión starts with the feeling or reaction: it matters to me a lot

Spanish often allows this kind of flexibility more than English.

Yes.

Even though an English speaker may feel that me is somehow central, the grammatical subject is tu opinión.

You can test it by changing singular to plural:

• Tu opinión me importa
• Tus opiniones me importan

The verb changes according to opinión/opiniones, so that is the subject.

Yes. That is also correct, but it is slightly different in style.

• Tu opinión me importa mucho is very natural and idiomatic.
• Tu opinión es muy importante para mí is a bit more explicit and sometimes sounds slightly more formal or deliberate.

Both express a similar idea, but the first one is a very common everyday Spanish way to say it.

You would usually say:

• Su opinión me importa mucho

Here su means your in the formal usted form.

So:

• Tu opinión... = informal, talking to someone you use tú with
• Su opinión... = formal, talking to someone you use usted with

In Spain, this distinction is still important depending on the situation and the relationship.

No. In this sentence, tu already determines the noun, so you do not use an article.

• tu opinión = correct
• la tu opinión = incorrect

This is similar to English, where you say your opinion, not the your opinion.

A simple pronunciation guide is:

too oh-pee-NYON meh eem-POR-tah MOO-choh

A few points:

• tu sounds like too
• opinión is stressed on the last syllable: nyon
• importa is stressed on por
• mucho in Spain has the same ch sound as in church

So the rhythm is:

tu o-pi-NIÓN me im-POR-ta MU-cho