La amikino, kies telefono ne funkciis hieraŭ, sendis al mi mesaĝon hodiaŭ matene.

The suffix -in- marks female sex. So:

• amiko = friend
• amikino = female friend

So la amikino tells you that the friend is female. In modern Esperanto, amiko is often used as a general friend, while amikino is specifically female.

La is the definite article, like the in English. It shows that the speaker has a specific friend in mind.

So:

• amikino = a female friend
• la amikino = the female friend

In this sentence, the speaker is talking about a particular friend, not just any friend.

Kies means whose. It shows possession.

Here, kies telefono means whose phone.

This is different from kiu, which usually means who, which, or which one.
So:

• kiu asks or refers to identity
• kies asks or refers to ownership/possession

In this sentence, we need possession, because the phone belongs to the friend.

Because kies already acts like a determiner, similar to my, your, or whose in English.

In Esperanto, you normally do not use la together with that kind of word before the same noun:

• mia libro = my book, not la mia libro in ordinary use
• ŝia domo = her house
• kies telefono = whose phone

So kies telefono is the normal form.

No. Kies always stays kies.

The noun after it is the word that changes if needed:

• kies telefono = whose phone
• kies telefonoj = whose phones
• kies telefonon = whose phone as a direct object

So kies itself does not take -j or -n.

Because that part is a subordinate relative clause inserted into the main sentence.

Main clause:

• La amikino sendis al mi mesaĝon hodiaŭ matene.

Inserted relative clause:

• kies telefono ne funkciis hieraŭ

Esperanto regularly separates subordinate clauses with commas. Since this clause appears in the middle of the sentence, it gets a comma before it and a comma after it.

Telefono is the subject of funkciis.

So the structure is:

• kies = whose
• telefono = phone
• ne funkciis = did not work

In other words, it is the phone that did not function. The whole clause describes la amikino.

In Esperanto, ne usually goes directly before the word or phrase it negates.

Here it negates the verb:

• ne funkciis = did not work

That is the most normal placement. It clearly tells you that the phone was not functioning.

Because -is is the Esperanto past-tense ending.

• funkciis = worked / was functioning
• sendis = sent

Both actions happened in the past:

• the phone did not work yesterday
• the friend sent a message this morning

So both verbs correctly use the past tense.

Mesaĝon is the direct object, so it takes the accusative ending -n.

It is the thing that was sent:

• sendis mesaĝon = sent a message

But mi is not a direct object here. It comes after the preposition al:

• al mi = to me

After a preposition like al, you normally do not add -n. So:

• mesaĝon = direct object
• al mi = recipient

Because al marks the person receiving something.

With sendi, Esperanto commonly uses this pattern:

• sendi ion al iu = to send something to someone

So:

• mesaĝon = the thing sent
• al mi = to me

English can say sent me a message without to, but Esperanto normally uses al to show that relationship clearly.

Matene is an adverb, from mateno = morning.

The ending -e makes it mean something like in the morning or morning-time.

So:

• mateno = morning
• matene = in the morning

Then:

• hodiaŭ matene = today in the morning = this morning

That is a very natural Esperanto time expression.

Esperanto word order is fairly flexible, as long as the grammar is clear.

For example, these are also possible:

• La amikino sendis mesaĝon al mi hodiaŭ matene.
• Hodiaŭ matene la amikino sendis al mi mesaĝon.

The original order is helpful because:

• hieraŭ stays near ne funkciis, so it clearly belongs to the phone problem
• hodiaŭ matene stays near sendis, so it clearly belongs to the sending

So the order is not the only possible one, but it is clear and natural.