Tunica sororis non alba est, sed rubra.

Because sororis is the genitive singular form of soror, meaning of the sister or simply the sister’s.

So:

• soror = sister
• sororis = of the sister / sister’s

In tunica sororis, the genitive shows possession: the sister’s tunic.

Latin word order is much more flexible than English word order. Tunica comes first because it is the main thing being talked about.

The sentence is about the tunic, and then Latin adds more information about it:

• whose tunic? → sororis
• what is it not? → non alba
• what is it instead? → sed rubra

So placing tunica first gives it emphasis as the topic.

Because they agree with tunica, which is a feminine singular noun.

In Latin, adjectives must match the noun they describe in:

• gender
• number
• case

Since tunica is feminine singular nominative, the adjectives must also be feminine singular nominative:

• albus → masculine
• alba → feminine
• album → neuter

and similarly:

• ruber → masculine
• rubra → feminine
• rubrum → neuter

So alba and rubra are the correct forms to match tunica.

Because the subject is tunica, which is singular.

• tunica = the tunic
• est = is

If the subject were plural, Latin would use sunt instead:

• Tunica est = The tunic is
• Tunicae sunt = The tunics are

Latin often leaves out a word if it is easy to understand from context. This is called ellipsis.

So:

• Tunica sororis non alba est, sed rubra
  means
• The sister’s tunic is not white, but red

A fuller version would be:

• Tunica sororis non alba est, sed rubra est

But Latin does not need to repeat est, because the meaning is already clear.

Non negates the idea that the tunic is white.

So the sentence means:

• it is not white
• it is red instead

Because non comes before alba est, it naturally gives the meaning is not white.

Sed means but.

It introduces a contrast:

• non alba = not white
• sed rubra = but red

So sed is the perfect conjunction here because the sentence is correcting or contrasting one description with another.

Latin has no articles, so it does not directly mark the difference between the and a.

So sororis could grammatically mean:

• of the sister
• of a sister
• sister’s

In practice, the context usually tells you which is best in translation. English has to choose, but Latin does not.

Because they are predicate adjectives describing the subject tunica after the verb est.

In Latin, when an adjective is linked to the subject by a form of to be, it usually appears in the same case as the subject, here the nominative.

So:

• tunica = nominative subject
• alba = nominative adjective linked to tunica
• rubra = nominative adjective linked to tunica

This is similar to English in meaning:

• The tunic is white
• The tunic is red

Yes. Latin allows several word orders without changing the basic meaning, though the emphasis may change.

For example, you could also see:

• Sororis tunica non alba est, sed rubra
• Non alba est tunica sororis, sed rubra
• Tunica sororis rubra est, non alba

These all still mean essentially The sister’s tunic is not white, but red, but they place emphasis on different parts of the sentence.

The version Tunica sororis non alba est, sed rubra is a natural and clear way to say it.

Yes. It is a noun phrase made up of:

• tunica = the main noun
• sororis = a genitive modifier showing possession

Together they mean:

• the sister’s tunic
• literally, the tunic of the sister

This is a very common Latin pattern: noun + genitive.

• tunica is a first-declension noun.
• soror, sororis is a third-declension noun.

That is why their endings look different:

• tunica has the familiar first-declension nominative singular ending -a
• sororis has the third-declension genitive singular ending -is

So this sentence is a good example of how different declensions can work together in one phrase.