Kvankam mia patro ne konsentis tuj, li poste diris, ke via opinio estis la plej bona.

Kvankam means although / even though. It introduces a subordinate clause that gives a contrast:

• Kvankam mia patro ne konsentis tuj... = Although my father did not agree immediately...

This is different from sed, which means but and joins two main clauses:

• Mia patro ne konsentis tuj, sed li poste diris... = My father did not agree immediately, but he later said...

So kvankam is more like although, while sed is more like but.

The commas mark the boundaries between clauses.

• Kvankam mia patro ne konsentis tuj,
  The first comma closes the kvankam clause.
• li poste diris, ke via opinio estis la plej bona.
  The second comma comes before the clause introduced by ke = that.

Esperanto often uses commas quite regularly before subordinate clauses such as those introduced by ke, kvankam, ĉar, and so on.

In Esperanto, ne usually comes directly before the word or phrase it negates. Here it negates the verb:

• ne konsentis = did not agree

So mia patro ne konsentis tuj means my father did not agree immediately.

Tuj means immediately, right away, or at once.

So:

• ne konsentis tuj = did not agree right away

It does not mean now. For now, Esperanto uses nun.

Konsenti can be used intransitively, so it does not need a direct object.

Here, ne konsentis tuj simply means did not agree immediately or did not consent immediately.

If you want to specify more, Esperanto often uses prepositions:

• konsenti kun iu = to agree with someone
• konsenti pri io = to agree about something
• konsenti al io = to agree to something

But in your sentence, leaving it without an object is perfectly normal.

The ending -is marks the past tense in Esperanto.

So:

• konsentis = agreed
• diris = said
• estis = was

The whole sentence is narrated in the past, so all three verbs are past-tense forms. Esperanto keeps tense marking very regular: one ending per tense, regardless of person.

Ke means that and introduces a subordinate clause:

• li poste diris, ke via opinio estis la plej bona
  = he later said that your opinion was the best

Unlike English, where that is often omitted, Esperanto normally keeps ke in sentences like this. So diris ke... is the standard pattern.

Because via opinio is the subject of estis.

In Esperanto, the -n ending marks a direct object, not a subject. Here the structure is:

• via opinio = the thing being talked about
• estis la plej bona = was the best

So:

• via opinio estis... = your opinion was...

not

• vian opinion estis... which would be wrong

Plej forms the superlative: most, best, etc.

• bona = good
• pli bona = better
• la plej bona = the best

The article la is normally used when you mean the best out of a group. In this sentence, the idea is that among the possible opinions, your opinion was the best one.

Because bona is a predicate adjective after estis.

After verbs like esti (to be), the adjective describes the subject and does not take -n:

• La domo estas granda = The house is big
• Via opinio estis la plej bona = Your opinion was the best

So bona agrees with opinio in number and case, but since opinio is not an object here, there is no -n.

Not completely. Esperanto word order is fairly flexible, though some orders sound more natural than others.

For example, you could also say:

• Kvankam mia patro ne konsentis tuj, poste li diris...
• Li poste diris...
• Poste li diris...

These all work, but the original word order is very natural and clear. Esperanto relies a lot on endings like -n and verb endings, so word order can move around more than in English.