Mi malfermas la kurtenon en la mateno, por ke pli da lumo venu en la ĉambron.

Because la kurtenon is the direct object of malfermas.

• Mi malfermas = I open / I am opening
• What am I opening? la kurtenon = the curtain

In Esperanto, the direct object usually takes -n. This is called the accusative ending.

Compare:

• La kurteno estas blanka. = The curtain is white.
• Mi malfermas la kurtenon. = I open the curtain.

So kurteno becomes kurtenon because it is receiving the action.

Kurtenon is singular: the curtain.
Kurtenojn would be plural: the curtains.

So the sentence is talking about one curtain, or it is simply phrased that way for the example. If you wanted plural, you could say:

• Mi malfermas la kurtenojn... = I open the curtains...

English often uses curtains in situations where Esperanto might use either singular or plural, depending on what the speaker is imagining.

Because after por ke, Esperanto normally uses the volitive/subjunctive-style verb ending -u.

• por ke = so that / in order that
• venu = may come / might come / come

So:

• por ke pli da lumo venu... = so that more light may come...

This is not the ordinary present tense. It expresses purpose, intention, or something wanted.

A very common pattern is:

• Mi faras tion, por ke... = I do that so that...

Examples:

• Mi fermas la pordon, por ke la kato ne eniru.
  = I close the door so that the cat won’t come in.

Because the second part has its own verb: venu.

• por is used before a noun phrase or infinitive:

  • por helpi = to help
  • por la infanoj = for the children

• por ke is used when there is a full clause with a subject and verb:

  • por ke pli da lumo venu = so that more light comes / may come

You can think of it like this:

• por + infinitive/noun
• por ke + finite verb

Both can sometimes express purpose, but here por ke is the natural choice because pli da lumo venu en la ĉambron is a complete clause.

Because da is used after words of quantity like pli, multe, iom, sufiĉe, etc.

• pli da lumo = more light
• multe da akvo = a lot of water
• iom da pano = some bread

So da links the quantity word to the thing being measured.

Lumo here is treated as a mass noun, like light in English, so pli da lumo is the normal form.

In this sentence, da means something like of after a quantity expression.

So:

• pli da lumo literally = more of light
• natural English = more light

Esperanto uses da when you are talking about how much of something there is.

Common examples:

• glaso da akvo = a glass of water
• multe da homoj = many people / a lot of people
• pli da tempo = more time

So in your sentence, pli da lumo means a greater amount of light.

Great question. After prepositions, Esperanto sometimes adds -n to show direction toward a place.

So there is an important difference:

• en la ĉambro = in the room (location)
• en la ĉambron = into the room (movement/direction)

Here the light is not simply located in the room; it is coming into the room. That is why ĉambron takes -n.

Compare:

• La kato estas en la ĉambro. = The cat is in the room.
• La kato kuras en la ĉambron. = The cat runs into the room.

So venu en la ĉambron means come into the room.

They are very close in meaning.

• en la mateno = in the morning
• matene = in the morning / mornings / in a morning way, depending on context

In many situations, either one would work.

Differences:

• en la mateno is a little more explicitly like English in the morning
• matene is a simple adverb formed from mateno

So you could also say:

• Mi malfermas la kurtenon matene...

That would sound natural too.

In Esperanto, -as is the present tense, but it does not make the same strict distinction English does between:

• I open
• I am opening

So Mi malfermas can mean either one, depending on context.

It can describe:

• a general habit: I open the curtain in the morning
• a current action: I’m opening the curtain now

Because the sentence includes en la mateno, many learners will naturally understand it as a habitual action: I open the curtain in the morning...

The subject is pli da lumo.

So the structure is:

• por ke pli da lumo venu en la ĉambron
• so that more light may come into the room

Esperanto does not need a dummy subject like English it here. The real subject is already present: more light.

Also, lumo is singular in grammar, so the verb is singular too:

• lumo venu = light may come

Yes. Esperanto word order is fairly flexible, though some orders sound more natural than others.

The original sentence is very natural:

• Mi malfermas la kurtenon en la mateno, por ke pli da lumo venu en la ĉambron.

You could also see variants such as:

• En la mateno mi malfermas la kurtenon...
• Mi malfermas en la mateno la kurtenon...

The first one is especially natural if you want to emphasize in the morning.

Even though Esperanto allows flexibility, learners should usually prefer the most straightforward order until they feel comfortable with the language.