Lunde mi kutime iras al la oficejo frue.

Here Lunde means on Monday. Because the sentence also has kutime (usually), the overall sense is on Mondays or usually on Monday.

So:

• Lunde = on Monday
• Lunde ... kutime ... = a habitual action, so English often makes it On Mondays, I usually...

The -e ending makes it an adverb. With days of the week, Esperanto often uses adverb forms to mean on that day.

For example:

• lundo = Monday
• lunde = on Monday
• mardo = Tuesday
• marde = on Tuesday

So lunde is not just the noun Monday; it is the adverbial form meaning on Monday.

Because Esperanto does not need one here. The form lunde already includes the idea of on Monday.

English says:

• on Monday

Esperanto often says simply:

• lunde

This is a very normal pattern with days of the week.

No. In Esperanto, days of the week are normally not capitalized unless normal sentence rules require it.

So:

• lunde in the middle of a sentence
• Lunde at the beginning of a sentence

It is capitalized here only because it is the first word.

Yes, by itself lunde can mean on Monday in a general sense, and context decides whether it is:

• a specific Monday, or
• Mondays in general

In this sentence, kutime makes it clear that this is a habitual action, so English would usually understand it as on Mondays.

In Esperanto, verb endings show tense, but they do not change for person the way they do in some languages.

So:

• mi iras = I go / I am going
• vi iras = you go / you are going
• li iras = he goes / he is going

Because iras is the same for all persons, the subject pronoun is usually needed:

• mi = I

Kutime means usually. It is an adverb that tells you the action is habitual, not a one-time event.

So:

• mi iras = I go / I am going
• mi kutime iras = I usually go

It modifies the whole action of going to the office.

Because the Esperanto present tense -as is used both for:

• actions happening now, and
• general or habitual actions

So iras can mean:

• am going
• go
• usually go

The adverb kutime tells you that the habitual meaning is intended here.

Because al means to / toward, showing movement in the direction of the office.

Compare:

• Mi iras al la oficejo. = I go to the office.
• Mi estas en la oficejo. = I am in the office.

So:

• al = movement toward a place
• en = being inside a place

La is the definite article, meaning the.

Here la oficejo means the office, usually a specific office that is understood from context, such as:

• my office
• the office where I work
• the office we both know about

Without la, oficejo would sound less specific.

Because it is not the direct object of the verb, and the preposition al already shows direction.

In this sentence:

• iras = go
• al la oficejo = to the office

So oficejo stays without -n.

A useful comparison:

• Mi vidas la oficejon. = I see the office.
  Here oficejon gets -n because it is a direct object.
• Mi iras al la oficejo. = I go to the office.
  Here oficejo is part of a prepositional phrase, not a direct object.

Frue means early. It ends in -e because it is an adverb.

Compare:

• frua = early, early-related (an early train)
• frue = early (to arrive early)

In this sentence, frue describes how / when the going happens:

• I usually go to the office early.

Yes. Esperanto word order is fairly flexible, especially with adverbs like lunde, kutime, and frue.

This sentence could also appear as:

• Mi kutime iras al la oficejo lunde frue.
• Kutime mi iras al la oficejo frue lunde.
• Frue lunde mi kutime iras al la oficejo.

These all keep roughly the same basic meaning, though the emphasis changes a little. The original sentence is natural and clear.

Yes, you sometimes can. Lundon can also mean on Monday, using the accusative of time.

So both of these can work:

• Lunde mi kutime iras al la oficejo frue.
• Lundon mi kutime iras al la oficejo frue.

However, with days of the week, the -e form like lunde is especially common and straightforward.

Mostly it modifies iras: it tells you that the action of going happens early.

So the core idea is:

• I usually go to the office early on Monday / on Mondays.

Because adverbs are flexible, frue can feel like it describes the timing of the whole situation, but grammatically it is functioning as an adverb of the action iras.