Mi esperas, ke la kurso estos interesa kaj utila.

Because Esperanto verbs do not change according to the subject the way English verbs sometimes do.

The ending -as always marks the present tense:

• mi esperas = I hope
• vi esperas = you hope
• li/ŝi esperas = he/she hopes
• ili esperas = they hope

So esperas is the correct present-tense form for every person.

Ke means that and introduces a subordinate clause.

So:

• Mi esperas = I hope
• ke la kurso estos interesa kaj utila = that the course will be interesting and useful

In English, that is sometimes optional:

• I hope that the course will be interesting
• I hope the course will be interesting

In Esperanto, ke is normally used when introducing this kind of clause.

Estos is the future tense of esti (to be).

The forms of esti are:

• estas = is/am/are
• estis = was/were
• estos = will be

So:

• la kurso estos interesa = the course will be interesting

It is future because the speaker is talking about what they hope the course will be, not what it already is now.

Because they are adjectives.

In Esperanto:

• nouns end in -o
• adjectives end in -a
• adverbs end in -e

So:

• kurso = course, a noun
• interesa = interesting, an adjective
• utila = useful, an adjective

These adjectives describe la kurso.

Because they are not direct objects here. They are predicate adjectives after the verb esti.

In la kurso estos interesa kaj utila:

• la kurso is the subject
• estos is the verb
• interesa kaj utila describes the subject

Also, la kurso is singular, so the adjectives stay singular too.

If the noun were plural, the adjectives would agree:

• la kursoj estos interesaj kaj utilaj = the courses will be interesting and useful

Because la kurso is the subject of the clause, not the direct object.

In the sentence:

• Mi esperas is the main clause
• ke la kurso estos interesa kaj utila is a subordinate clause

Inside that subordinate clause, la kurso is the thing that will be interesting and useful, so it is the subject.

The direct object of esperas is really the whole ke-clause, not the single noun kurso.

Because ke introduces a subordinate clause, and Esperanto normally separates that with a comma.

So:

• Mi esperas, ke ...

This is very standard punctuation in Esperanto.

La is the definite article, meaning the.

So:

• kurso = a course / course
• la kurso = the course

It refers to a specific course, probably one already known from the context.

Normally, no. That would sound unnatural here.

If you mean the course or a specific course, you use la kurso.

If you wanted a more general idea, you would usually still phrase it differently, for example:

• Mi esperas, ke la kurso estos interesa kaj utila. = I hope the course will be interesting and useful.
• Mi esperas, ke iu kurso estos interesa kaj utila. = I hope some course will be interesting and useful.

So in this sentence, la kurso is the natural choice.

Yes. Kaj means and.

Here it joins two adjectives:

• interesa kaj utila = interesting and useful

Both adjectives describe la kurso.

Yes. You could also say:

• Mi esperas, ke la kurso estos utila kaj interesa.

That would still be grammatical. The meaning is basically the same, though the order can slightly change what feels more emphasized.

Not completely, but this is the most natural and straightforward order.

Standard order:

• Mi esperas, ke la kurso estos interesa kaj utila.

Because Esperanto marks grammar with endings, word order is somewhat flexible. But learners should usually stick to the normal order unless there is a special reason to change it.

Because Esperanto normally uses a ke-clause after esperi when expressing a full idea like this.

So:

• Mi esperas, ke la kurso estos interesa kaj utila.

This is the normal way to say I hope that the course will be interesting and useful.

Using an infinitive after esperi would not express this sentence naturally.

In Esperanto, stress is always on the second-to-last syllable of each word.

So the main stresses are:

• MI
• es-PE-ras
• KE
• la KUR-so
• ES-tos
• in-te-RE-sa
• KAJ
• u-TI-la

That regular stress pattern is one of the nice things about Esperanto pronunciation.

Yes. After Mi esperas, ke..., Esperanto normally uses the ordinary tense that fits the meaning.

Here the speaker hopes about the future, so we get:

• estos = will be

Esperanto does have a -u form, but it is not used here. The sentence is simply stating what the speaker hopes will happen:

• Mi esperas, ke la kurso estos interesa kaj utila.

That is the normal construction.