Unus modius tritici satis est ad panem, sed pater dicit plus hordei servandum esse.

Because unus modius is the subject of est.

• modius is a masculine second-declension noun.
• The subject must be in the nominative singular, so we get modius.
• unus agrees with it in case, number, and gender, so it is also nominative singular masculine.

If it were a direct object, you would expect unum modium instead.

This is a very common Latin pattern: a word of quantity or measure is followed by a genitive showing what is being measured.

So:

• modius tritici = a peck / measure of wheat
• plus hordei = more barley

This genitive is often called the partitive genitive or a genitive used with expressions of quantity.

satis is an indeclinable word meaning enough or sufficiently. With est, it means:

• is enough
• is sufficient

So unus modius tritici satis est means that one measure of wheat is sufficient.

Latin uses satis very naturally in this way, even though English may sometimes prefer a fuller phrasing.

Yes. Although ad often means to or toward, it can also express purpose, use, or fitness for.

So ad panem here means something like:

• for bread
• for making bread
• for bread use

Also, ad always takes the accusative, which is why the noun is panem.

Because hordeum is treated as a mass noun here, like barley in English.

• plus is the normal word for more with uncountable stuff or quantity.
• plures is used for more people or more countable items.

So:

• plus hordei = more barley
• but plures servi = more slaves

Grammatically, plus is a neuter singular comparative form used substantively, and it takes a genitive: hordei.

After verbs of saying, thinking, knowing, hearing, and similar verbs, Latin usually uses indirect statement rather than a clause introduced by that.

English:

• Father says that more barley must be stored.

Latin:

• pater dicit plus hordei servandum esse

This construction uses:

• a subject accusative
• plus an infinitive

Here, the whole reported statement is packed into plus hordei servandum esse.

servandum esse is the passive periphrastic, a very common Latin way to express necessity or obligation.

It is made from:

• the gerundive: servandum
• plus esse

So it means:

• must be stored
• must be kept
• ought to be preserved

This is stronger than a plain infinitive like servare (to store / to keep). The gerundive adds the idea of something needing to be done.

Because it agrees with plus, which is grammatically neuter singular.

Even though plus hordei is translated as more barley, the head word is actually plus, and hordei depends on it in the genitive. So the gerundive matches plus:

• plus = neuter singular
• servandum = neuter singular

This can be confusing because in English we focus on barley, but Latin grammar is really built around plus.

It is there: plus is functioning as the subject of the indirect statement.

After dicit, Latin normally uses an accusative subject plus infinitive. The tricky part is that plus has the same form for nominative and accusative neuter singular, so it does not visibly change.

So in pater dicit plus hordei servandum esse:

• plus = accusative subject of the indirect statement
• servandum esse = infinitive phrase

Because the neuter singular nominative and accusative look the same, the construction can seem less obvious than with a word like servum or puellam.

The sentence does not say explicitly.

Latin can name the person responsible in a passive periphrastic by using the dative of agent, for example:

• nobis plus hordei servandum est = we must store more barley

But here there is no such dative, so the idea is simply:

• more barley must be stored

The context would tell you who is expected to do it.