La prelego de la profesoro pri la historio de la urbo estis tiel klara, ke eĉ lacaj studentoj atente aŭskultis.

A useful way to read it is in three chunks:

• La prelego de la profesoro pri la historio de la urbo = the subject noun phrase
• estis tiel klara = the main predicate, was so clear
• ke eĉ lacaj studentoj atente aŭskultis = the result clause, that even tired students listened attentively

So the sentence structure is basically:

[The professor's lecture about the city's history] [was so clear] [that even tired students listened attentively].

In Esperanto, la is the definite article, meaning the. It does not change for gender, number, or case.

It appears several times here because several nouns are definite:

• la prelego = the lecture
• la profesoro = the professor
• la historio = the history
• la urbo = the city

Esperanto often repeats la where English might also use the, and sometimes even where English might be a little looser.

De is a very common preposition meaning things like of, from, or sometimes indicating authorship/association.

Here:

• la prelego de la profesoro = the professor's lecture / the lecture by the professor
• la historio de la urbo = the history of the city

So Esperanto uses de where English often uses apostrophe-s or of.

Pri means about or concerning.

So:

• prelego pri la historio de la urbo = a lecture about the history of the city

This tells you the topic of the lecture.

That is different from de:

• de la profesoro tells you whose lecture it is / who gave it
• pri la historio de la urbo tells you what the lecture is about

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

In this sentence:

• estis tiel klara = was so clear
• ke eĉ lacaj studentoj atente aŭskultis = that even tired students listened attentively

So the pattern is:

• tiel + adjective/adverb + ke
• so + adjective/adverb + that

This is a very common Esperanto construction.

Because adjectives in Esperanto agree with the nouns they describe.

• prelego is singular, so klara is singular
• studentoj is plural, so lacaj is plural

Compare:

• klara prelego = a clear lecture
• lacaj studentoj = tired students

If a noun is plural, the adjective also gets -j.

Because studentoj is the subject of aŭskultis, not a direct object.

In Esperanto, -n usually marks the direct object.

Here:

• studentoj aŭskultis = students listened

So studentoj is doing the action.

If you included the thing they listened to, that object would take -n:

• la studentoj aŭskultis la prelegon = the students listened to the lecture

In the original sentence, the object is left unstated because it is easy to understand from context.

Because atente is an adverb.

In Esperanto:

• -a = adjective
• -e = adverb

So:

• atenta = attentive
• atente = attentively

Here atente modifies the verb aŭskultis, telling us how they listened.

Yes. Even though aŭskulti often takes an object, Esperanto can leave the object out when it is obvious or unimportant.

Here, the listener naturally understands that they listened to the lecture.

So atente aŭskultis works fine as listened attentively.

Because of both word order and meaning.

The phrase is:

• pri la historio de la urbo

That naturally groups as:

• the history of the city

So the whole larger phrase is:

• the professor's lecture
  about [the history of the city]

It would be much less natural to understand it as the lecture of the city. Also, pri clearly introduces the topic phrase, and inside that phrase de la urbo most naturally modifies historio.

In this context, it can suggest either the professor's lecture or the lecture given by the professor.

Esperanto de covers a broad range of relationships that English may express in different ways. So here it indicates that the lecture belongs to, is associated with, or was given by the professor.

Usually context makes the intended meaning clear, and here both English phrasings point to the same basic idea.