Alexandria urbs clarissima est.

Yes, they are both nouns. Here urbs is in apposition to Alexandria. That means it gives extra information about the same thing:

• Alexandria = the name of the city
• urbs = city

So Alexandria urbs clarissima est means something like Alexandria, a very famous city, is... or more naturally Alexandria is a very famous city.

Latin often places two nouns next to each other like this when they refer to the same person or thing.

Alexandria is in the nominative case because it is the subject of the sentence.

The sentence is saying something about Alexandria: Alexandria ... est = Alexandria is ...

Since urbs refers to the same thing as Alexandria, it is also nominative.

Because it is in apposition with Alexandria.

In Latin, when two nouns refer to the same thing, they usually stand in the same case. Since Alexandria is nominative, urbs is nominative too.

So:

• Alexandria = nominative subject
• urbs = nominative appositive noun
• clarissima = nominative adjective agreeing with urbs

Clarissima is the superlative form of clarus.

• clarus = famous, clear, distinguished
• clarior = more famous
• clarissimus / clarissima / clarissimum = most famous, very famous

So clarissima can mean:

• most famous
• or sometimes simply very famous

In this sentence, English usually translates it naturally as a very famous city or the most famous city, depending on context.

Because clarissima must agree with urbs.

Urbs is:

• feminine
• singular
• nominative

So the adjective must also be:

• feminine
• singular
• nominative

That gives clarissima.

Grammatically, clarissima agrees with urbs, because urbs is a regular noun with clear gender: feminine.

But since urbs and Alexandria refer to the same thing, the meaning applies to Alexandria too. So in sense it describes the whole idea Alexandria, the city.

This is very common in Latin: the adjective agrees with the noun it is attached to, even if another noun nearby refers to the same thing.

Est means is. It is the third person singular present form of esse, to be.

So:

• est = is

It links the subject to what is being said about it:

• Alexandria ... est = Alexandria is ...

Latin does not have definite or indefinite articles like English the and a/an.

So urbs clarissima could be understood in different ways depending on context:

• a very famous city
• the very famous city
• the most famous city

English has to choose an article when translating, but Latin does not need one.

It is a perfectly normal Latin word order, but Latin word order is much freer than English word order.

This sentence could also appear in other orders, such as:

• Alexandria clarissima urbs est
• Urbs clarissima Alexandria est

The basic relationships stay clear because of case endings and agreement, not just position.

Still, the given order is straightforward and natural:

• name first
• identifying noun next
• descriptive adjective
• verb at the end

Yes, it could, depending on context.

The superlative clarissima can mean either:

• most famous
• or very famous

Latin superlatives do not always have to be taken in a strict comparison sense. Sometimes they simply intensify the adjective.

So without more context, both are grammatically possible, though many learners are first taught to read it as Alexandria is a very famous city.

Alexandria is treated as feminine, and that fits well because urbs is feminine too.

Many city names in Latin are feminine, especially when understood as urbs. In this sentence, the presence of urbs makes the feminine idea very clear.

That is another reason why clarissima appears in the feminine form.

Yes, that would also be a possible Latin sentence.

Alexandria clarissima est would mean Alexandria is very famous or Alexandria is most famous.

Including urbs makes the statement more specific:

• Alexandria clarissima est = Alexandria is very famous
• Alexandria urbs clarissima est = Alexandria is a very famous city

So urbs adds the idea of city explicitly.