Sed mater respondet rumorem saepe falsum esse et rationem quaeri oportere.

After respondet, Latin is using indirect statement (also called the accusative-and-infinitive construction).

So instead of saying:

• the rumor is often false
• an explanation ought to be sought

with normal finite verbs, Latin puts them into reported form:

• rumorem saepe falsum esse
• rationem quaeri oportere

A very literal pattern is:

• mater respondet = the mother replies
• rumorem ... esse = that the rumor is ...
• rationem ... oportere = that it is proper/necessary ...

This is extremely common after verbs of saying, thinking, knowing, hearing, and so on.

Because in an indirect statement, the subject of the reported clause usually goes into the accusative.

So:

• direct statement: rumor falsus est = the rumor is false
• indirect statement after respondet: rumorem falsum esse = that the rumor is false

Likewise:

• direct statement: ratio quaeritur = an explanation is sought
• with oportet: rationem quaeri oportet = an explanation ought to be sought
• indirect statement after respondet: rationem quaeri oportere = that an explanation ought to be sought

So rumorem and rationem are not random objects here. They are accusative because they are the subjects of reported statements.

Because indirect statement requires an infinitive, not a finite verb.

In a direct statement you would say:

• rumor falsus est = the rumor is false

But after respondet, Latin changes est to esse:

• rumorem falsum esse = that the rumor is false

So esse is simply the infinitive form corresponding to est in this construction.

Because falsum agrees with rumorem.

Here rumorem is:

• masculine
• singular
• accusative

So the adjective must match it:

• rumorem falsum

If this were a direct statement, you would get nominatives:

• rumor falsus est

But in indirect statement both the noun and its agreeing adjective shift into the accusative:

• rumorem falsum esse

Because the two infinitives are doing two different jobs.

• oportere is infinitive because the whole clause is in indirect statement after respondet
• quaeri is infinitive because it depends on oportere

Think of the direct version first:

• rationem quaeri oportet = an explanation ought to be sought

Now put that into indirect statement after respondet:

• rationem quaeri oportere = that an explanation ought to be sought

So the stacking is perfectly normal:

• quaeri = to be sought
• oportere = to be proper/necessary

In effect: that it is necessary for an explanation to be sought

No. It is better understood as the subject of the passive infinitive quaeri.

Compare:

• active: aliquis rationem quaerit = someone seeks an explanation
• passive: ratio quaeritur = an explanation is sought

In indirect statement, that subject becomes accusative:

• rationem quaeri = that an explanation is sought

So even though rationem is accusative, it is not functioning like a normal direct object here. It is the accusative subject of the infinitive clause.

Because the meaning is general: an explanation should be sought, without naming who should seek it.

Latin often uses the passive for this kind of idea, especially with verbs like oportet.

Compare:

• aliquem rationem quaerere oportet = someone ought to seek an explanation
• rationem quaeri oportet = an explanation ought to be sought

The passive version is less personal and more general, which fits the sentence well.

Oportere means something like:

• to be proper
• to be right
• to be necessary
• ought

In smoother English, rationem quaeri oportere is naturally rendered as:

• that an explanation ought to be sought
• that one should look for an explanation

So oportere expresses obligation or appropriateness, but often in a somewhat impersonal way.

That is a very common question, because ratio has a wide range of meanings.

Depending on context, ratio can mean:

• reason
• explanation
• method
• plan
• account
• calculation

Here, with quaeri (to be sought), the sense is something like:

• reason
• explanation
• the real explanation behind the rumor

So if the meaning shown to the learner is an explanation should be sought, that is a perfectly natural understanding of rationem here.

Because Latin word order is much freer than English word order.

Saepe is an adverb meaning often, and it modifies the idea falsum esse:

• rumorem saepe falsum esse = that the rumor is often false

Latin can place adverbs in several reasonable positions. Here saepe sits inside the indirect statement, close to what it modifies.

So the order is not strange once you get used to Latin flexibility. The grammar is carried mostly by endings, not by fixed position.

Yes. In Latin, verbs like respondere can introduce reported content, much like say, reply, or answer that ... in English.

So:

• mater respondet ... = the mother replies/answers that ...

Even if English might sometimes prefer says or replies that, Latin respondet works fine with an indirect statement.

The important thing for the learner is that once Latin treats something as reported content after a verb like this, the language normally switches into the accusative-and-infinitive pattern.