Avus dicit cor bonum veritatem amare.

Because after dicit in Latin, a reported statement is often expressed with an indirect statement construction rather than a full clause with that.

So instead of saying:

• Avus dicit quod cor bonum veritatem amat = Grandfather says that a good heart loves truth

Latin more commonly says:

• Avus dicit cor bonum veritatem amare

In this pattern:

• the verb of the reported statement goes into the infinitive: amare = to love
• the subject of that reported statement goes into the accusative

So cor bonum veritatem amare means literally something like a good heart to love truth, but in proper English it means that a good heart loves truth.

Latin often does not use a separate word equivalent to English that when reporting what someone says, thinks, hears, or knows.

English says:

• Grandfather says that a good heart loves truth

Latin usually uses the accusative + infinitive construction instead:

• dicit cor bonum veritatem amare

So the idea of that is built into the grammar of the indirect statement. You do not need a separate word for it.

Because cor is a neuter third-declension noun, and for many neuter nouns, the nominative and accusative singular look the same.

Its principal forms are:

• cor = nominative singular
• cordis = genitive singular

In this sentence, cor is functioning as the subject of the infinitive amare inside an indirect statement, so grammatically it is accusative. But the accusative singular of cor is also cor.

So even though the form looks unchanged, its function is accusative here.

Because bonum has to agree with cor.

• cor is neuter
• cor is singular
• in this sentence it is accusative in function within the indirect statement

So the adjective must also be:

• neuter
• singular
• accusative

That gives bonum.

Compare:

• bonus = masculine singular
• bona = feminine singular, or neuter plural depending on context
• bonum = neuter singular

Since cor is neuter singular, bonum is the correct form.

Because veritatem is the direct object of amare.

The verb amare means to love, and the thing being loved goes into the accusative. Here, that thing is truth:

• veritas = truth
• veritatem = truth, as direct object

So:

• cor bonum veritatem amare = a good heart loves truth

Within that reported statement:

• cor bonum = subject
• veritatem = object
• amare = infinitive verb

There are really two layers in the sentence.

1. The main sentence

• Avus dicit = Grandfather says

Here, avus is the subject of dicit.

2. The reported statement

• cor bonum veritatem amare = that a good heart loves truth

Here, cor bonum is the subject of amare.

So:

• subject of dicit: avus
• subject of amare: cor bonum

This is a very common thing in Latin: one subject belongs to the main verb, and another belongs to the infinitive inside an indirect statement.

Yes. This is one of the most important Latin sentence patterns.

After verbs like:

• dicit = says
• putat = thinks
• scit = knows
• audit = hears

Latin often uses:

• accusative subject + infinitive verb

In your sentence:

• cor bonum = accusative subject of the indirect statement
• amare = infinitive

So this is a classic accusative-and-infinitive construction, often abbreviated as ACI.

Because the forms and meanings point the other way.

• veritatem is clearly accusative singular feminine
• bonum agrees with cor, forming the phrase cor bonum = good heart
• amare takes a direct object, and veritatem fits naturally as that object

Also, semantically:

• a good heart loves truth makes clear sense
• truth loves a good heart would require different forms and would not match the sentence as written

So the grammar and the meaning both support:

• cor bonum = subject of amare
• veritatem = object of amare

Latin word order is more flexible than English because Latin relies more on endings than on position.

English normally needs a fixed order:

• Grandfather says that a good heart loves truth

Latin can move words around more freely:

• Avus dicit cor bonum veritatem amare
• Avus cor bonum veritatem amare dicit
• Veritatem avus dicit cor bonum amare

These can all express basically the same idea, though the emphasis may change.

In your sentence, the order is quite natural:

• Avus = subject first
• dicit = main verb
• then the indirect statement
• amare at the end, which is a very common place for a verb in Latin

Sometimes yes, especially in later Latin, but in standard Classical Latin the accusative-and-infinitive construction is the normal choice after dicit.

So Classical Latin strongly prefers:

• Avus dicit cor bonum veritatem amare

A clause with quod is possible in some kinds of Latin, but a learner should recognize that the infinitive construction is the standard one to expect here.

A learner often wants to identify each word by its dictionary entry. Here they are:

• avus, avi — grandfather
• dico, dicere, dixi, dictum — say, tell
• cor, cordis — heart
• bonus, bona, bonum — good
• veritas, veritatis — truth
• amo, amare, amavi, amatum — love

This helps you see where the forms in the sentence come from:

• avus from avus
• dicit from dico
• cor from cor
• bonum from bonus, bona, bonum
• veritatem from veritas
• amare from amo