Pater tamen dicit mustum diu servandum non esse in sole.

Because this is an indirect statement after dicit.

After verbs of saying, thinking, knowing, and the like, Latin often uses:

• accusative subject
  • infinitive

So in:

• Pater tamen dicit mustum ... non esse in sole

the thing being talked about, mustum, becomes the subject of the infinitive esse, and subjects of infinitives in this construction go into the accusative.

So:

• direct idea: Mustum non est servandum in sole = The must should not be kept in the sun
• reported after dicit: Pater dicit mustum non esse servandum in sole = Father says that the must should not be kept in the sun

It is a gerundive + esse construction, often called the passive periphrastic.

This usually expresses:

• necessity
• obligation
• what ought to be done

So:

• servandum est = it must be kept / it should be kept

Since servandum agrees with mustum, the full idea is:

• mustum servandum esse = that the must should be kept / that the must must be kept

With non:

• mustum servandum non esse = that the must should not be kept

Because servandum agrees with mustum.

Mustum is:

• neuter
• singular
• accusative

So the gerundive must match it:

• servandum = neuter singular accusative

Agreement is the key here. If the noun were different, the gerundive would change too:

• vinum servandum
• aqua servanda
• panis servandus

In this sentence, mustum controls the form.

In meaning, both would normally give the same basic idea:

• servandum non esse
• non servandum esse

Both mean roughly:

• that it is not to be kept
• that it should not be kept

Latin word order is flexible, so the position of non often depends on style or emphasis more than on a major change in meaning.

Here, servandum non esse is a perfectly normal way to express the negated passive periphrastic inside indirect statement.

Diu is an adverb meaning:

• for a long time
• long

It modifies the idea of serving/keeping, not dicit.

So the sense is:

• mustum diu servandum non esse
• that the must should not be kept for a long time

It tells you the duration of the keeping.

In sole means in the sun.

Here:

• in
  • ablative (sole) indicates location

So:

• in sole = in the sun
• compare in horto = in the garden
• compare in aqua = in the water

This is different from in + accusative, which often indicates motion into something.

Tamen usually means:

• however
• nevertheless
• still

It adds a contrast with something previously said or expected.

So Pater tamen dicit... suggests something like:

• Father, however, says...
• Father still says...

The exact English wording depends on context, but the core idea is contrast.

Because Latin usually does not use a separate word for that in this kind of reported statement.

English says:

• Father says that the must should not be kept in the sun

Latin instead uses the accusative-and-infinitive construction:

• Pater dicit mustum ... non esse...

So the idea of English that is built into the grammar of:

• accusative subject (mustum)
• infinitive (esse)

Latin often expresses grammar through case and infinitive structure rather than with an extra connecting word.

Yes. That would be a direct statement rather than reported speech.

• Mustum non est diu servandum in sole = The must should not be kept in the sun for a long time

After dicit, Latin changes that direct statement into indirect statement:

• Pater dicit mustum diu servandum non esse in sole

The main changes are:

• mustum becomes accusative
• est becomes infinitive esse

That is a very common pattern in Latin.

The sentence does not say.

The passive periphrastic often focuses on what ought to be done, not on who must do it.

So:

• mustum servandum est = the must must be kept / the must should be kept

This leaves the agent unstated.

If Latin wanted to say who had the obligation, it could use a dative of agent:

• nobis mustum servandum est = we must keep the must

But in your sentence, the speaker is only giving the rule, not naming the responsible person.

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

Latin often arranges words for:

• emphasis
• rhythm
• clarity
• style

Here, the sentence groups related ideas together:

• mustum = the thing being discussed
• diu servandum non esse = the main verbal idea
• in sole = the place

An English learner may want something like:

• Pater tamen dicit mustum non esse diu servandum in sole

and that would still be understandable Latin. But the given order is natural and idiomatic.

In Latin, you should look first for:

• the main verb: dicit
• the infinitive construction after it: mustum ... non esse
• the gerundive expressing necessity: servandum
• the adverb and phrase: diu, in sole

That helps more than trying to read the sentence in strict English order.