Lumea este frumoasă.

Because Romanian usually puts the definite article at the end of the noun.

• lume = world
• lumea = the world

So -a here is the definite article, roughly equivalent to English the. This is a very common Romanian pattern.

Este means is. It is the 3rd person singular present form of a fi, which means to be.

So:

• eu sunt = I am
• tu ești = you are
• el/ea este = he/she is

In this sentence, este links the subject lumea to the description frumoasă.

Because Romanian adjectives must agree with the noun they describe in gender and number.

Lumea is feminine singular, so the adjective must also be feminine singular:

• masculine singular: frumos
• feminine singular: frumoasă
• masculine plural: frumoși
• feminine plural: frumoase

Even after este, the adjective still agrees with the subject.

Yes. That is very common and completely correct.

• este = fuller, slightly more formal or careful
• e = shorter, very common in everyday speech

So both are good:

• Lumea este frumoasă.
• Lumea e frumoasă.

A rough pronunciation guide is:

LOO-mea ES-te froo-MWOA-suh

More carefully:

• lu in lumea sounds like loo
• ș in frumoasă sounds like sh
• ă sounds like the a in English sofa
• oa in frumoasă is a glide, something like woa

Approximate stress:

• LU-mea
• ES-te
• fru-MOA-să

If you know IPA, one possible transcription is /ˈlu.me̯a ˈes.te fruˈmo̯a.sə/.

Not always. Lumea can also mean things like:

• people
• everyone
• the public

For example:

• Lumea spune că... = People say that...

But in this sentence, the most natural meaning is the world.

Because this is a normal subject + verb + predicate adjective structure:

• Lumea = subject
• este = verb
• frumoasă = predicate adjective

This is the most neutral word order, similar to English The world is beautiful.

Romanian can change word order for emphasis, for example:

• Frumoasă este lumea.

That sounds more poetic or emphatic, not the most basic neutral order for a learner to copy first.

Because Romanian usually attaches the definite article to the noun instead of putting it in front.

Compare:

• English: the world
• Romanian: lumea

This is one of the biggest differences from English. The article is often a suffix in Romanian.

Because frumoasă is a predicate adjective, not a noun.

After a fi (to be), Romanian normally uses the adjective directly:

• Lumea este frumoasă.
• Fata este frumoasă.

You do not put an article there the way you would with a noun phrase.

In a normal complete sentence, no. You need a form of to be:

• Lumea este frumoasă.
• Lumea e frumoasă.

Without este/e, it would not sound like a normal complete statement. It would sound incomplete or very unusual outside poetry or special stylistic contexts.

They are Romanian diacritics, and they matter.

• ș = the sh sound
• ă = a short neutral vowel, like the a in sofa

So frumoasă is standard Romanian spelling. In informal typing, people sometimes leave diacritics out, but proper writing should include them.

A negative sentence:

• Lumea nu este frumoasă.
• Lumea nu e frumoasă.

A yes/no question can be made with intonation:

• Lumea este frumoasă?

Or with a different word order:

• Este lumea frumoasă?

Both are understandable, but the first keeps the original sentence structure and simply adds question intonation.