Sur la tabulo estas skribitaj tri ĝustaj respondoj, kaj unu eraro jam estas trovita.

Yes. estas skribitaj is the present passive.

• skribi = to write
• skribitaj = written (past passive participle, plural)
• estas skribitaj = are written / have been written

So:

• tri ĝustaj respondoj estas skribitaj = three correct answers are written

In natural English, depending on context, this may mean:

• three correct answers are written on the board
• three correct answers have been written on the board

Esperanto often uses this very regular passive structure:

• estas + passive participle

The same thing happens later in the sentence:

• unu eraro jam estas trovita = one error has already been found

Because it agrees with tri ĝustaj respondoj, which is plural.

In Esperanto, adjectives and participles used like adjectives must agree with the noun in:

• number: singular or plural
• case: nominative or accusative

Here:

• tri respondoj = three answers → plural
• so ĝustaj = correct, plural
• and skribitaj = written, plural

That is why you see:

• tri ĝustaj respondoj
• estas skribitaj

If the noun were singular, you would have:

• unu ĝusta respondo estas skribita

Because it agrees with unu eraro, which is singular.

• unu eraro = one error
• so the participle must also be singular:
• estas trovita = is found / has been found

Compare:

• unu eraro jam estas trovita = one error has already been found
• du eraroj jam estas trovitaj = two errors have already been found

Because both are the subjects of passive clauses, not direct objects.

A learner might expect respondojn because in English answers feels like the thing being written. But in this sentence the structure is passive:

• tri ĝustaj respondoj estas skribitaj
  = three correct answers are written

Here tri ĝustaj respondoj is the grammatical subject, so it stays in the nominative, with no -n.

Likewise:

• unu eraro jam estas trovita
  = one error has already been found

Again, unu eraro is the subject.

If you changed it to active voice, then you might get an accusative object:

• Iu skribis tri ĝustajn respondojn sur la tabulo.
  = Someone wrote three correct answers on the board.

There, respondojn gets -n because it is the direct object.

Esperanto word order is quite flexible. Starting with Sur la tabulo puts the location first for emphasis or scene-setting:

• Sur la tabulo estas skribitaj tri ĝustaj respondoj
  literally: On the board are written three correct answers

This is completely normal Esperanto.

A more straightforward order would also be possible:

• Tri ĝustaj respondoj estas skribitaj sur la tabulo.

Both are grammatical. The version with Sur la tabulo first sounds a bit more descriptive, like presenting what is visible on the board.

sur la tabulo means on the board.

• sur = on, on top of, on the surface of
• tabulo = board

A blackboard or whiteboard is treated as a surface, so Esperanto uses sur.

So:

• sur la tablo = on the table
• sur la muro = on the wall
• sur la tabulo = on the board

Using en la tabulo would mean something like in the board, which is not what you want here.

jam means already.

So:

• unu eraro estas trovita = one error is found / has been found
• unu eraro jam estas trovita = one error has already been found

It adds the idea that this has happened by now, perhaps earlier than expected or before something else.

In context, it suggests progress:

• there are three correct answers written on the board,
• and one error has already been found.

Because jam is an adverb, and in Esperanto adverbs often go before the verb or verb phrase they modify.

So:

• unu eraro jam estas trovita

is a very normal way to say:

• one error has already been found

You may also see adverbs in slightly different positions depending on emphasis, but this placement is standard and natural.

ĝusta usually means correct, right, or accurate.

So:

• ĝusta respondo = correct answer

This is the most natural choice here.

korekta exists too, but it often means correct in form, proper, or in accordance with rules, and it is less idiomatic in many everyday situations. For answers to a question, ĝusta respondo is the usual phrase.

So tri ĝustaj respondoj simply means:

• three correct answers

Yes. In context, that is often the best English translation.

Esperanto passive forms do not always match English tense choices one-to-one in a simple mechanical way. Here:

• estas skribitaj can often be understood as are written or have been written
• estas trovita can often be understood as is found or has been found

Because the sentence describes the current state resulting from earlier actions, English often prefers:

• On the board, three correct answers have been written, and one error has already been found.

Or more naturally:

• Three correct answers are written on the board, and one error has already been found.

The exact English choice depends on style and context.

Yes. Esperanto can express the same idea in active voice, but the focus changes.

Passive version:

• Sur la tabulo estas skribitaj tri ĝustaj respondoj, kaj unu eraro jam estas trovita.

This focuses on:

• the answers on the board
• the error that has been found

An active version would need an agent, for example:

• Iu skribis tri ĝustajn respondojn sur la tabulo, kaj iu jam trovis unu eraron.
  = Someone wrote three correct answers on the board, and someone has already found one error.

The passive is useful when the doer is unknown, unimportant, or deliberately left unstated. That is very common in Esperanto, just as in English.