Hoc ornamentum pretiosius est quam illud.

Because hoc has to agree with ornamentum in gender, number, and case.

• ornamentum is neuter
• singular
• nominative here

The demonstrative hic, haec, hoc means this, but its form changes:

• hic = masculine
• haec = feminine
• hoc = neuter

Since ornamentum is a neuter noun, Latin uses hoc.

It is nominative singular.

That is because hoc ornamentum is the subject of est:

• hoc ornamentum = the thing being talked about
• est = is
• pretiosius = the description being given about the subject

So the basic structure is:

Hoc ornamentum | pretiosius est
This ornament | is more precious

Because pretiosius is the neuter nominative singular form of the comparative adjective.

The comparative of pretiosus (precious) is:

• pretiosior for masculine/feminine
• pretiosius for neuter

Since ornamentum is neuter, the adjective must also be neuter:

• masculine: liber pretiosior
• feminine: gemma pretiosior
• neuter: ornamentum pretiosius

So pretiosius agrees with ornamentum.

Yes, pretiosius already means more precious.

Latin usually does not need a separate word for more when using a comparative adjective. The comparative ending itself carries that meaning.

So:

• pretiosus = precious
• pretiosius = more precious

That is why the sentence does not need a separate word equivalent to English more.

Quam means than in a comparison.

It links the two things being compared:

• hoc ornamentum = this ornament
• illud = that one / that ornament
• pretiosius est quam illud = is more precious than that one

So quam is the standard word Latin uses for this kind of comparison.

Because Latin can leave out a noun when it is obvious from the context.

Here, illud really means something like:

• that one
• or that ornament

The noun ornamentum is understood, so it does not need to be repeated.

This is very common in Latin. English does something similar when we say:

• This ornament is more expensive than that one.

Latin simply uses illud where English might say that one.

Here illud is best understood as nominative singular neuter, with ornamentum understood.

So the comparison is basically:

• hoc ornamentum
• quam illud ornamentum

Both sides are in the same case, which is very normal after quam.

Also, illud is neuter singular because the omitted noun is ornamentum, which is neuter singular.

Yes. Latin often has two ways to make this kind of comparison.

This sentence uses:

• comparative + quam
• pretiosius quam illud

But Latin can also use the ablative of comparison:

• Hoc ornamentum illo pretiosius est.

That means the same thing: This ornament is more precious than that one.

So both patterns are common:

1. pretiosius quam illud
2. illo pretiosius

Not as much as it would be in English. Latin word order is relatively flexible because the endings show how the words relate to each other.

So this sentence could appear in slightly different orders, for example:

• Hoc ornamentum pretiosius est quam illud.
• Hoc ornamentum quam illud pretiosius est.
• Pretiosius est hoc ornamentum quam illud.

These can all mean the same basic thing, though the emphasis may shift a little.

The given order is straightforward and natural:

• subject first
• then the comparative adjective and verb
• then the quam phrase

A simple breakdown is:

• hoc = this, demonstrative adjective agreeing with ornamentum
• ornamentum = ornament, the subject
• pretiosius = more precious, predicate adjective
• est = is, the linking verb
• quam = than
• illud = that one / that ornament, the second item in the comparison

So the core structure is:

subject + predicate adjective + verb + comparison

That is a very common Latin pattern.