Vendredon mia fratino restos hejme, ĉar ŝi jam promesis helpi nian avinon.

Here -n is not marking a direct object. It is the accusative of time, which Esperanto often uses for expressions like on Friday, last week, all day, and so on.

So:

• vendredo = Friday
• vendredon = on Friday

A native English speaker often expects a preposition like on, but Esperanto can simply use the accusative ending instead.

Yes. Vendrede is also a normal way to say on Friday.

So these are both possible:

• Vendredon mia fratino restos hejme.
• Vendrede mia fratino restos hejme.

The difference is mostly stylistic here. Learners should just know that Esperanto has more than one common way to express time.

The ending -os marks the future tense in Esperanto.

So:

• resti = to stay, to remain
• restas = stays / is staying
• restis = stayed
• restos = will stay

So mia fratino restos hejme means my sister will stay home.

Hejmo is the noun home.
Hejme is an adverb meaning at home.

In this sentence, the idea is location, not the noun itself:

• hejmo = home
• hejme = at home

So:

• resti hejme = to stay at home

This is very common in Esperanto. Some place-related words are often used in adverb form to express location.

Because the promise happened earlier.

The sentence says that on Friday the sister will stay home, because she already promised to help their grandmother. So the two times are different:

• restos = future action
• promesis = earlier action, already completed

Esperanto tense endings show the time of each verb clearly:

• -is = past
• -as = present
• -os = future

So this sentence is very natural: the staying home is future, but the promise was made before now.

Jam means already.

So ŝi jam promesis means she has already promised or she already promised.

It adds the idea that the promise is not new and has already been made, which explains why she will stay home on Friday.

Because helpi is the infinitive form, meaning to help.

After promesi (to promise), Esperanto normally uses an infinitive:

• promesi helpi = to promise to help

So:

• ŝi promesis helpi = she promised to help

This works much like English.

Because nian avinon is the direct object, and adjectives must agree with the noun they describe.

Breakdown:

• avino = grandmother
• avinon = grandmother as direct object
• nia = our
• nian = our, agreeing with a noun that has -n

So:

• helpi nian avinon = to help our grandmother

In Esperanto, adjectives and adjective-like words such as possessives agree with the noun in number and case.

Ĉar means because.

It introduces the reason:

• Vendredon mia fratino restos hejme = On Friday my sister will stay home
• ĉar ŝi jam promesis helpi nian avinon = because she already promised to help our grandmother

So ĉar works much like English because.

Esperanto word order is fairly flexible. Putting Vendredon first emphasizes the time or sets the scene first:

• Vendredon mia fratino restos hejme... = On Friday, my sister will stay home...
• Mia fratino restos hejme vendredon... would also be understandable, though less natural to many speakers.

Starting with the time expression is very common, especially when the speaker wants to frame the whole sentence around when something happens.

In this sentence:

• ĉ in ĉar sounds like ch in church
• ŝ in ŝi sounds like sh in shoe

So roughly:

• ĉar ≈ char
• ŝi ≈ shee

Esperanto spelling is very regular, so these sounds stay consistent from word to word.