Pater dicit lac ex vacca, quam filia mulget, calidum esse.

After a verb like dicit (says), Latin very often uses an indirect statement construction:

• subject of the reported statement in the accusative
• verb of the reported statement in the infinitive

So lac ... calidum esse means the milk to be warm, which English naturally turns into that the milk is warm.

That is why Latin has esse rather than est here.

Yes. In this sentence, lac is the subject of the infinitive esse, so in Latin indirect statement it must be accusative.

The reason it looks unchanged is that lac is a neuter noun, and its nominative and accusative singular are the same form:

• nominative: lac
• accusative: lac

So the case changes, but the spelling does not.

Calidum agrees with lac:

• lac is neuter
• singular
• accusative in this construction

So the adjective must also be neuter singular accusative: calidum.

And because the sentence is using indirect statement, the verb is esse, not est.

So:

• lac calidum est = the milk is warm
• dicit lac calidum esse = he says that the milk is warm

Vacca is ablative singular because it follows the preposition ex, which takes the ablative.

So:

• ex vacca = from the cow

This phrase tells you the source of the milk.

Because the case of a relative pronoun depends on its job inside its own clause, not on the case of the noun it refers to.

Here quam refers back to vacca, but inside the clause quam filia mulget it is the object of mulget:

• filia milks the cow
• therefore the relative pronoun must be accusative
• so Latin uses quam

Even though vacca itself is ablative after ex, the relative pronoun does not copy that case automatically.

It describes vacca.

A good way to see that is the gender:

• quam is feminine singular
• vacca is feminine singular
• lac is neuter, so quam cannot refer to lac

So the phrase means the cow which the daughter milks, not the milk which the daughter milks.

Because filia is the subject of mulget in the relative clause.

In quam filia mulget:

• filia = the daughter = the one doing the milking = nominative
• quam = the cow = the thing being milked = accusative

So the clause is structured as:

• the daughter milks the cow

Latin word order is much more flexible than English word order because the endings show how the words function.

So Latin can place the relative clause right after vacca:

• lac ex vacca, quam filia mulget, calidum esse

This keeps quam filia mulget close to the noun it describes, vacca.

Also, Latin often puts the infinitive phrase toward the end of the sentence, so calidum esse naturally comes late.

Not very much. They are mainly there to help the reader.

The commas mark off the relative clause:

• quam filia mulget

Latin grammar here depends on the word forms and endings, not on the punctuation. Even without commas, the sentence would still work grammatically.