Mi ĝojas pri via mesaĝo.

Because ĝoji is a verb meaning to be glad / to rejoice. In Esperanto, many feelings can be expressed either with a verb or with esti + adjective.

So:

• Mi ĝojas = I am glad / I’m happy
• Mi estas ĝoja = I am glad / I’m happy

Both are correct.
The version with ĝojas feels very natural and common.

Pri usually means about, concerning, or regarding.

In this sentence, it shows what you are glad about:

• Mi ĝojas pri via mesaĝo = I am glad about your message.

This is a very common pattern:

• ĝoji pri io = to be glad about something

So it is best to learn ĝoji pri as a set pattern.

Because via mesaĝo is not a direct object here.

Esperanto adds -n for the accusative, mainly for direct objects. But after a preposition like pri, you normally do not use -n.

So:

• pri via mesaĝo = about your message

not

• pri vian mesaĝon

Also, adjectives and possessives agree with the noun, so since mesaĝo has no -n, via does not get one either.

For the same reason: pri is a preposition, and nouns after ordinary prepositions normally stay in the basic form, without -n.

Compare:

• Mi legas vian mesaĝon. = I read your message.

  • Here mesaĝon is a direct object, so it takes -n.

• Mi ĝojas pri via mesaĝo. = I am glad about your message.

  • Here mesaĝo comes after pri, so there is no -n.

Yes. That is completely correct.

There is a small style difference:

• Mi ĝojas pri via mesaĝo = uses the verb ĝoji
• Mi estas ĝoja pri via mesaĝo = uses esti
  • adjective ĝoja

In many situations, they mean almost the same thing.
The first one is often a little more direct and idiomatic.

Here is the breakdown:

• Mi = I
• ĝoj- = the root meaning joy / gladness
• -as = present tense verb ending
• pri = about / concerning
• via = your
• mesaĝ-o = message
  
  • mesaĝ- = message
  • -o = noun ending

So the sentence is built very regularly, which is typical Esperanto.

It can mean both.

Esperanto does not distinguish:

• your (one person)
• your (more than one person)

Both are simply via.

If needed, the context tells you which one is meant.

The normal order is:

• Mi ĝojas pri via mesaĝo.

But Esperanto word order is fairly flexible, especially for emphasis. For example:

• Pri via mesaĝo mi ĝojas.

This puts extra focus on via mesaĝo.

Even so, the standard neutral order is the original one, and that is usually the best choice for learners.

The special letter ĝ is pronounced like the j in job or gem.

So ĝojas sounds approximately like:

• JOY-as

And mesaĝo is approximately:

• meh-SAH-zho

A few helpful points:

• ĝ = English j sound
• ĵ would be like the s in measure, but that letter does not appear here
• Esperanto stress is usually on the second-to-last syllable

So:

• ĜO-jas
• me-SA-ĝo

Because Esperanto normally does not use la before possessives like via, mia, lia, and so on.

So you say:

• via mesaĝo = your message

not usually:

• la via mesaĝo

This is similar to English, where we say your message, not the your message.