Mi konas instruistinon, kies lecionoj estas tiel interesaj, ke eĉ lacaj studentoj atente aŭskultas.

Because instruistinon is the direct object of mi konas.

• mi = I
• konas = know
• instruistinon = a female teacher

In Esperanto, the direct object takes -n. So:

• Mi konas instruistino would be wrong.
• Mi konas instruistinon = I know a female teacher

You can also break the word apart:

• instru- = teach
• -ist- = a person who does something professionally or regularly
• -in- = female
• -o = noun
• -n = accusative/direct object

So instruistinon literally means female teacher as the object of the verb.

Kies means whose.

So:

• instruistinon, kies lecionoj... = a female teacher whose lessons...

A very important point: kies does not change its ending. It stays kies whether the thing possessed is singular, plural, subject, or object.

Examples:

• kies libro = whose book
• kies libroj = whose books
• kies amikon = whose friend (as object)

In this sentence, kies connects instruistinon with lecionoj:

• the teacher, whose lessons...

Because lecionoj is the subject of estas.

The part kies lecionoj estas tiel interesaj means:

• whose lessons are so interesting

Here:

• lecionoj = lessons
• estas = are
• interesaj = interesting

Since lecionoj is the subject, it takes -j for plural, but not -n.

You would use -n only if lessons were the direct object of a verb.

Because adjectives in Esperanto agree with the nouns they describe.

• lecionoj = lessons (plural)
• therefore interesaj = interesting (plural)

Esperanto adjectives match nouns in number and case:

• interesa leciono = an interesting lesson
• interesaj lecionoj = interesting lessons
• interesajn lecionojn = interesting lessons (as direct object)

Here, lecionoj is plural, so interesaj must also be plural.

Tiel ... ke means so ... that.

In the sentence:

• tiel interesaj, ke eĉ lacaj studentoj atente aŭskultas

this means:

• so interesting that even tired students listen attentively

This is a common Esperanto pattern:

• tiel granda, ke... = so big that...
• tiel bone, ke... = so well that...
• tiel laca, ke... = so tired that...

So here:

• lecionoj estas tiel interesaj = the lessons are so interesting
• ke eĉ lacaj studentoj atente aŭskultas = that even tired students listen attentively

Because both kies and ke introduce subordinate clauses.

1. kies lecionoj estas tiel interesaj is a relative clause describing the teacher.
2. ke eĉ lacaj studentoj atente aŭskultas is a subordinate clause showing the result.

Esperanto commonly uses commas to separate such clauses, and in this sentence they help show the structure very clearly:

• Mi konas instruistinon,
• kies lecionoj estas tiel interesaj,
• ke eĉ lacaj studentoj atente aŭskultas.

So the commas are not random punctuation; they mark clause boundaries.

Because lacaj studentoj is the subject of aŭskultas.

The clause means:

• even tired students listen attentively

Here:

• studentoj = students
• lacaj = tired

Since studentoj is the subject, it is nominative, not accusative. So:

• lacaj studentoj = tired students

If they were the direct object, then you would use -n:

• Mi vidas lacajn studentojn = I see tired students

But in this sentence, the students are the ones doing the listening.

Because it describes how the students listen, not what the students are like.

• atente = attentively
• atentaj = attentive

Compare:

• Studentoj atente aŭskultas = Students listen attentively.
  Here atente describes the action aŭskultas.

• Studentoj estas atentaj = Students are attentive.
  Here atentaj describes the students themselves.

In Esperanto, adverbs usually end in -e, and adjectives end in -a.

An explicit object is not necessary here if the meaning is clear from context.

Aŭskulti means to listen or to listen to. In this sentence, the idea is that the students listen attentively during the teacher's lessons. The object is understood, even though it is not stated.

English does something similar:

• The students listened attentively.

You do not have to say exactly what they listened to if the context already tells you.

So the sentence is natural as it stands.

Yes, koni and scii are different, and English speakers often ask about this.

• koni = to know a person, place, language, or something through familiarity
• scii = to know a fact, to know that..., to be aware of information

So:

• Mi konas instruistinon = I know a teacher / I am acquainted with a teacher
• Mi scias, ke ŝi estas instruistino = I know that she is a teacher

In this sentence, the speaker is acquainted with the teacher, so konas is the correct verb.

Because instruistino specifically means female teacher.

• instruisto = teacher
• instruistino = female teacher

Esperanto uses -in- to mark female beings:

• patro = father
• patrino = mother
• frato = brother
• fratino = sister

So the sentence specifically says the speaker knows a female teacher, not just a teacher of unspecified sex.

Yes. A chunk-by-chunk reading is very helpful:

• Mi konas instruistinon = I know a female teacher
• kies lecionoj = whose lessons
• estas tiel interesaj = are so interesting
• ke = that
• eĉ lacaj studentoj = even tired students
• atente aŭskultas = listen attentively

Put together:

I know a female teacher whose lessons are so interesting that even tired students listen attentively.

This sentence is a good example of how Esperanto builds meaning very systematically:

• main clause
• relative clause
• result clause

That makes it long, but also very logical.