Ni ne ĉiam konsentas unu kun la alia, sed via opinio tamen gravas por mi.

Because ne ĉiam means not always.

• Ni ne ĉiam konsentas = We do not always agree
• literally: It is not always true that we agree

If you said Ni ĉiam ne konsentas, that would sound like We always do not agree, which is basically We never agree. Esperanto would usually express that more naturally as Ni neniam konsentas.

So:

• ne ĉiam = not always
• neniam = never

Konsenti means to agree.

It often works without a direct object:

• Ni konsentas. = We agree.

If you want to say what you agree about, you usually use pri:

• Ni konsentas pri la plano. = We agree about the plan.

If you want to say with whom you agree, you use kun:

• Mi konsentas kun vi. = I agree with you.

In your sentence, the idea of with each other is expressed by unu kun la alia, so there is no direct object.

Literally, it means one with the other.

In natural English, that becomes with each other or with one another.

So:

• Ni konsentas unu kun la alia = We agree with each other

This is a common Esperanto way to express a reciprocal idea when a preposition is needed.

This is an important distinction.

• unu kun la alia = with each other
• unu la alian = each other as a direct object

Use unu la alian when the verb takes a direct object:

• Ni vidas unu la alian. = We see each other.
• Ni helpas unu la alian. = We help each other.

Use unu kun la alia when Esperanto needs the preposition kun:

• Ni parolas unu kun la alia. = We speak with each other.
• Ni konsentas unu kun la alia. = We agree with each other.

So the form depends on the grammar of the verb.

Because via opinio is the subject of gravas.

In Esperanto, -n marks the direct object. But here, your opinion is not an object; it is the thing that matters / is important.

• Via opinio gravas por mi.
• literally: Your opinion matters to me

If you used vian opinion, that would make it a direct object, which would not fit this sentence.

Tamen means nevertheless, still, or all the same.

• sed = but
• tamen = nevertheless / still

Using both together strengthens the contrast:

• Ni ne ĉiam konsentas unu kun la alia, sed via opinio tamen gravas por mi.
• We do not always agree with each other, but your opinion still matters to me.

So sed introduces the contrast, and tamen emphasizes that the second statement remains true despite the first.

You could omit tamen, but the sentence would feel slightly less emphatic.

Yes. Gravas is the verb form gravi, meaning to be important or to matter.

So these are very close in meaning:

• Via opinio gravas por mi.
• Via opinio estas grava por mi.

Both are correct.

The version with gravas is a little more compact and often feels very natural in Esperanto.

In this kind of sentence, por mi is the usual choice for important to me / matters to me.

• grava por mi
• gravas por mi

This expresses that something is important from my point of view or in relation to me.

A learner should generally remember:

• Tio gravas por mi. = That matters to me.

Even if another phrasing might sometimes be understood, por mi is the standard, safe choice here.

Because kun is a preposition, and after a preposition you normally do not use the accusative -n.

So:

• kun la alia = with the other
• not kun la alian

That is why the phrase is unu kun la alia.

A useful rule for beginners is:

• direct object -> often -n
• after a preposition like kun, por, pri, en -> normally no -n

Yes. Esperanto word order is fairly flexible, although some versions sound more natural than others.

Your sentence is very natural as written:

• Ni ne ĉiam konsentas unu kun la alia, sed via opinio tamen gravas por mi.

You could also say:

• Ni ne ĉiam konsentas unu kun la alia, sed tamen via opinio gravas por mi.
• Ni ne ĉiam konsentas unu kun la alia, sed via opinio gravas por mi tamen.
  This is possible, but less natural in ordinary style.

Placing tamen before gravas or near the start of the second clause usually sounds best, because it clearly marks the contrast.

Yes: ĉ in ĉiam.

• ĉ is pronounced like ch in church
• so ĉiam sounds roughly like CHEE-am

Also remember that Esperanto stress normally falls on the second-to-last syllable:

• NI ne ĈI-am kon-SEN-tas U-nu kun la A-li-a, sed VI-a o-PI-ni-o TA-men GRA-vas por MI

You do not need to reduce vowels the way English often does; Esperanto vowels are pronounced clearly.