Pax in urbe servanda est.

They are:

• pax, pacis — peace
• urbs, urbis — city
• servo, servare, servavi, servatus — to preserve, keep, save
• sum, esse, fui — to be

So servanda comes from servo, and est comes from sum.

Because pax is the subject of the Latin sentence.

Latin is using a construction that literally means something like peace is to be preserved in the city. In that structure, the thing that must be preserved becomes the grammatical subject, so it stands in the nominative.

An English speaker may expect an object, as in we must preserve peace, but Latin often expresses this idea differently.

Servanda is a gerundive, sometimes also called the future passive participle.

In this sentence, it means something like to be preserved or needing to be preserved.

So:

• servanda est = must be preserved / is to be preserved

This is a very common Latin way of expressing necessity or obligation.

Because servanda has to agree with pax.

Pax is:

• feminine
• singular
• nominative

So the gerundive must also be:

• feminine
• singular
• nominative

That gives servanda.

If the noun were masculine, you would expect servandus. If it were neuter, servandum.

Together, servanda est forms part of the passive periphrastic, a construction that expresses obligation or necessity.

So pax servanda est means:

• peace must be preserved
• literally, peace is to be preserved

Latin often uses this structure where English uses must.

Because Latin does not always need one.

In this sentence, the idea of must is built into the combination:

• gerundive
  • form of esse

So:

• servanda est already contains the sense must be preserved

Latin can also use other ways to express necessity, but this is one of the standard and most important ones.

Because in with the ablative usually means in or inside a place.

So:

• in urbe = in the city

Here the sentence describes location, not movement.

Compare:

• in urbe = in the city
• in urbem = into the city

That is why urbe is ablative, not accusative.

Yes. In this construction, the person on whom the obligation falls is often put in the dative.

For example:

• civibus pax in urbe servanda est

This means the citizens must preserve peace in the city, or more literally, peace is to be preserved in the city by the citizens, with the idea of obligation falling on civibus.

That dative of the person obliged is very common with the passive periphrastic.

The basic meaning is very similar: both mean peace must be preserved in the city.

But the grammar is different:

• servanda est uses the gerundive + esse
• servari debet uses the passive infinitive servari with debet

The first is a very characteristic Latin way to express obligation. The second is also possible, but servanda est is often felt to be the more idiomatic classical pattern in sentences like this.

Latin word order is more flexible than English word order, because the endings show the grammatical relationships.

This order puts pax first, which gives it emphasis. The phrase in urbe then adds the setting, and servanda est comes at the end, where Latin often places the verbal idea.

Other orders are possible, but this one is natural and clear. The meaning does not depend mainly on position; it depends mainly on the word endings.