Esta obra de arte es moderna.

Because obra is a feminine singular noun, and the demonstrative has to agree with it.

• esta = this (for feminine singular nouns)
• este = this (for masculine singular nouns)

Since the main noun is obra, you say esta obra.

Obra de arte is a very common expression meaning work of art or artwork.

The de works like of in English:

• obra = work
• de arte = of art

So literally it is work of art. Spanish often uses de in noun phrases like this.

Use es because moderna is describing a general, inherent characteristic of the artwork, not a temporary condition or location.

• ser is used for identity, classification, and essential descriptions
• estar is used for location, temporary states, and conditions

So:

• Esta obra de arte es moderna. = This artwork is modern.
• Esta obra de arte está en el museo. = This artwork is in the museum.

Because moderna must agree with obra, which is feminine singular.

In Spanish, adjectives usually agree in gender and number with the noun they describe.

• obra = feminine singular
• moderna = feminine singular form of moderno

If the noun were masculine, you would use moderno.

It describes obra, not arte.

The main noun in the phrase is obra. The words de arte just tell you what kind of work it is: a work of art.

So the agreement is with obra:

• esta obra ... moderna

Even though arte is nearby, it is not the noun being described by moderna here.

Because esta already fills that determiner role.

In Spanish, you usually do not combine a demonstrative like esta with an indefinite article like una.

• esta obra = this work
• una obra = a work

So esta obra is correct, while esta una obra would be wrong.

Arte can be a little tricky for learners.

In the singular, when it appears with the definite article, standard Spanish often uses el arte, even though historically it has feminine roots. In practice, learners usually just remember:

• el arte moderno
• las artes modernas

But in your sentence, this does not affect moderna, because moderna agrees with obra, not arte.

Yes. That means The work of art is modern.

The difference is:

• Esta obra de arte es moderna. = This work of art is modern.
• La obra de arte es moderna. = The work of art is modern.

So the grammar is similar, but esta points to a specific item near the speaker or already being indicated.

Not much in this sentence if you want the same natural meaning.

The normal order is:

• Esta obra de arte es moderna.

That is: demonstrative + noun phrase + verb + adjective

You could move things around in special contexts for emphasis, but for a learner, this is the standard and most natural order.

Normally, no. It is written esta, without an accent.

Older spelling sometimes used ésta to distinguish the pronoun from the adjective, but current standard Spanish generally does not require that accent.

So in your sentence, esta obra de arte es moderna is the normal modern spelling.

A simple pronunciation guide is:

EH-stah OH-brah deh AHR-teh es moh-DER-nah

A few helpful notes:

• e is usually like the vowel in bet, but cleaner and shorter
• o is a pure oh sound
• r in obra is a tapped Spanish r
• h is silent, but there is no h in this sentence anyway

A more careful approximation: Es-ta o-bra de ar-te es mo-der-na

Yes, obra de arte is the standard, natural expression for work of art.

While pieza can mean piece, pieza de arte is much less common as a general equivalent in everyday use. If you want the usual phrase, obra de arte is the best choice.