La contingencia cambia el plan familiar de emergencia.

Because contingencia is a feminine singular noun, so it takes the feminine singular definite article la.

• el = masculine singular
• la = feminine singular
• los / las = plural

So la contingencia means the contingency.

Cambia is the third-person singular form of the verb cambiar in the present tense.

The subject is la contingencia, which is singular, so the verb must also be singular:

• yo cambio
• tú cambias
• él / ella / usted cambia

So La contingencia cambia... means The contingency changes...

Yes. In this sentence, cambiar is being used transitively, meaning it has a direct object.

• Subject: La contingencia
• Verb: cambia
• Direct object: el plan familiar de emergencia

So the structure is:

something changes something

Here, the contingency changes the family emergency plan.

Because plan is a masculine singular noun in Spanish, so it takes el.

Even though it ends in -n, not -o, it is still masculine:

• el plan
• el pan
• el tren

Grammatical gender in Spanish does not always match the word ending, so this just has to be learned with the noun.

No. Here familiar means related to the family or family as an adjective.

So:

• plan familiar = family plan

This is different from the English adjective familiar meaning well-known. Spanish familiar can sometimes also mean that, depending on context, but in this sentence it clearly means family-related.

In Spanish, adjectives often come after the noun, especially when they are classifying or describing a type of thing.

So:

• plan familiar = family plan
• coche eléctrico = electric car
• servicio público = public service

Putting familiar after plan is the normal order here.

De emergencia means for emergencies or emergency.

It modifies plan familiar, so el plan familiar de emergencia means something like:

• the family emergency plan
• literally, the family plan of emergency

Spanish often uses de + noun where English uses a noun as an adjective:

• plan de emergencia = emergency plan
• salida de emergencia = emergency exit
• botón de emergencia = emergency button

The most natural reading is that de emergencia modifies the whole noun phrase plan familiar.

So the idea is:

• a family emergency plan not
• a family plan that is emergency-like in some odd way

In practice, Spanish noun groups often build meaning step by step:

• plan
• plan familiar
• plan familiar de emergencia

Each new element narrows down the meaning.

Yes, that is also possible, and many speakers might even find it very natural depending on the intended emphasis.

There is a slight structural difference:

• plan familiar de emergencia = a family plan for emergencies
• plan de emergencia familiar = can sound like an emergency plan related to the family

Both are understandable, but plan familiar de emergencia clearly highlights that it is a family plan specifically for emergency situations.

Because el plan familiar de emergencia is the direct object, and Spanish does not normally use a before things.

The personal a is mainly used with specific people (and sometimes personified animals or very specific living beings), for example:

• Veo a María.
• Llamo a mi hermano.

But here the object is a thing, the plan, so there is no a:

• La contingencia cambia el plan...

Yes, Spanish word order is flexible, but the original order is the most neutral:

• La contingencia cambia el plan familiar de emergencia.

You could also say:

• El plan familiar de emergencia lo cambia la contingencia.

That version adds emphasis or contrast, but it is less neutral and more marked.

For learners, the basic subject + verb + object order is the safest choice.

Because the sentence is talking about one contingency, not several.

Compare:

• La contingencia cambia... = The contingency changes...
• Las contingencias cambian... = The contingencies change...

The article and the verb both change to match number:

• la / cambia = singular
• las / cambian = plural

It is a real and correct word, but it can sound a bit formal or technical depending on context.

In Spanish from Spain, contingencia may be used in areas such as:

• emergency planning
• official procedures
• insurance
• workplace safety
• risk management

In casual everyday speech, people might sometimes prefer more common words depending on the situation, such as problema, emergencia, imprevisto, or situación. But in formal or administrative language, contingencia fits very well.