It´s safe to say that the missing verb is:

establecieron (they established)

Let´s take a look at the full sentence:

Los misioneros establecieron las misiones para enseñarles su religión a los indígenas./ The missionaries established the missions to teach their religion to the indigenous people.

It´s safe to say that “descendencia” (ancestry) is the missing word.

Let´s take a look at the full fragment:

Sarita Montiel tiene antepasados italianos, españoles y portugueses. Ella es de descendencia europea./ Sarita Montiel has Italian, Spanish and Portuguese ancestors. She is of European ancestry.

The missing word is “imperio” (empire)

Let´s take a look at the phrases:

Los aztecas conquistaron muchos pueblos indígenas./ The Aztecs conquered many indigenous peoples.

Tenían un imperio muy grande./ They had a very large empire.

The missing word is desconocidas (adjective, plural, f.)/ unkown.

Let´s take a look at the phrases:

Cuando los españoles trajeron el chocolate y el maíz a Europa, nadie sabía lo que eran./ When the Spanish brought chocolate and corn to Europe, nobody knew what they were.

Eran mercancías desconocidas en Europa./ They were unknown goods in Europe.

The missing word is indígenas (adjective, plural, m.)/ indigenous

Let´s take a look at the full sentence:

Los aztecas, los toltecas y los mayas son pueblos indígenas de México./ The Aztecs, the Toltecs, and the Mayans are indigenous peoples of Mexico.

The missing word is poderosos (adjective, m. plural)/ powerful.

Let´s see the full sentence:

Los españoles pudieron conquistar el imperio azteca porque con sus armas de fuego y sus caballos eran más poderosos que los indígenas./ The Spanish were able to conquer the Aztec empire because with their firearms and their horses they were more powerful than the indigenous people.

The missing word is europeos (adjective, m., plural)/ European.

Let´s see the full sentence:

Francia, España, Inglaterra e Italia son países europeos./ France, Spain, England and Italy are European countries.

The missing word is colonia (noun, f., singular)/ colony.

Let´s take a look at the full sentence:

Cuando los españoles conquistaron el imperio azteca, México llegó a ser una colonia española y parte del imperio español./ When the Spanish conquered the Aztec empire, Mexico became a Spanish colony and part of the Spanish empire.

The missing word is: batallas (noun, f., plural)/ battles

Let´s take a look at the full sentence:

Los españoles y los indígenas lucharon en muchas batallas./ The Spanish and the Indians fought in many battles.

The missing word is se componen/ they´re composed of

Let´s take a look at the full sentence:

Muchas costumbres latinoamericanas se componen de elementos de culturas diferentes./ Many Latin American customs are made up of elements from different cultures.

The missing word is: adoptaron/ they adopted.

Hoy la mayor parte de los indígenas hispanoamericanos son católicos. Esto quiere decir que adoptaron la religión de los españoles./ Today most of the Hispanic American Indians are Catholic. This means that they adopted the religion of the Spanish.

The missing word is lengua/ language

En toda Hispanoamérica se empezó a hablar español, la lengua de España./ Spanish, the language of Spain, began to be spoken throughout Latin America.