Mi restos hejme dum du tagoj.

Restos comes from the verb resti, which means to stay, to remain, or to keep staying.

The ending -os is the Esperanto future tense. So:

• resti = to stay / to remain
• restas = stay(s) / am staying / is staying
• restis = stayed / was staying
• restos = will stay / will remain

So Mi restos means I will stay or I will remain.

Hejmo is the noun home.

But in this sentence, Esperanto uses hejme, which is an adverb-like form meaning at home. The ending -e is often used for adverbs or adverbial expressions.

So:

• hejmo = home
• hejme = at home

This is very common in Esperanto. Instead of saying something like in home, Esperanto often uses the -e form for places:

• hejme = at home
• lerneje = at school
• urbe = in the city / in town

So Mi restos hejme literally means I will stay at home.

Because Esperanto often expresses that idea with the -e ending instead of a preposition.

In English, you say at home. In Esperanto, hejme already contains that idea. So you do not need a separate word like at.

This is just a normal Esperanto pattern, not an omission.

Dum means during or for when talking about a length of time.

In this sentence, dum du tagoj means for two days.

Examples:

• Mi laboros dum tri horoj. = I will work for three hours.
• Ŝi dormis dum la tuta nokto. = She slept during the whole night.

So here, dum introduces the time span of the action.

Because after dum, the noun normally stays in its basic plural form: tagoj.

So:

• dum du tagoj = for two days

Esperanto also allows time expressions without a preposition, and then you often see the accusative:

• Mi restos du tagojn. = I will stay two days.

Both are possible, but they are built differently:

• dum du tagoj = using the preposition dum
• du tagojn = using the accusative of duration

In your sentence, since dum is already there, tagoj is correct.

Because du means two, so the noun must be plural.

In Esperanto, plural nouns end in -j:

• tago = day
• tagoj = days

So du tagoj means two days.

Because the sentence is talking about a duration, not a specific pair of days already identified as the two days.

So dum du tagoj simply means for two days.

If you said dum la du tagoj, that would mean something more like during the two days—usually referring to two specific days already known from context.

Compare:

• dum du tagoj = for two days
• dum la du tagoj = during the two days

Yes, Esperanto word order is fairly flexible, as long as the sentence stays clear.

The most neutral order is:

• Mi restos hejme dum du tagoj.

But you could also say:

• Dum du tagoj mi restos hejme.
• Hejme mi restos dum du tagoj.

These all mean basically the same thing, though the emphasis may shift slightly depending on what you put first.

The version with Mi first is the most straightforward and beginner-friendly.

Not necessarily. This is an important point.

Esperanto resti usually means to remain or to stay. It does not usually mean to relax the way English rest often does.

So in this sentence:

• Mi restos hejme = I will stay home / remain at home

If you want the idea of resting in the sense of relaxing, Esperanto more often uses verbs like ripozi.

So:

• resti = stay / remain
• ripozi = rest / relax

You probably could in a very literal sense, but it is not the normal way to say it.

Hejme is the natural Esperanto expression for at home.
En la hejmo sounds more like in the home/household or inside a specific home as a physical place, and it is less idiomatic in an everyday sentence like this.

So for normal speech, Mi restos hejme is the best choice.

Normally, yes, you include Mi.

In Esperanto, verbs do not change depending on the subject the way they do in some languages, so restos by itself does not tell you whether the subject is I, you, he, she, we, or they.

Because of that, subject pronouns are usually stated:

• Mi restos = I will stay
• Ŝi restos = she will stay
• Ili restos = they will stay

You can omit the pronoun only in special contexts where the subject is already completely obvious.