The school board's actions, described by the missing word, occur "despite the disapproval of many teachers." The correct answer needs to mean give support or approval, the definition of "endorsed."

The grandfather tells his grandchildren "wild stories." The correct answer needs to demonstrate the purpose of those tales. "Regale," meaning to entertain and amuse, is the best choice.

The use of a gift in the face of a son's anger means the father is trying to minimize the anger. The correct answer should mean to soothe or calm, the definition of "placate."

The subject does not "follow any rules," so any guidelines would be ignored or gone against. The correct answer must mean defied or rejected, the definition of "flouted."

If "success vindicated her," then presumably she had to be vindicated for something. This means her "unusual approach" was looked down on. "Disparaged," meaning to be criticized and dismissed, is the correct answer.

The fact the subject is a "national hero" means he is revered. The correct answer will indicate such a strong connection between the country and the subject. "Venerate," meaning to worship or revere, is the best choice.

Do not be tempted by "vacillations," which implies a back-and-forth motion. What is key here is to note the phrase "pass from one undertaking to another." This implies a passing from one thing to the next. This is best captured by "peregrinations." Although this strictly means a journey or pilgrimage in the physical sense (which would work as well in context, at least broadly speaking), taken metaphorically it is perfect.

The word comes from the Latin peregrinatio, meaning journey or pilgrimage. It is related to the root for words like "peregrine," which means foreign or wandering in English. Such words have at their base per and ager. The former is a preposition with many derivatives in English (e.g. "permanent", "perfect", "perturbed"). It means "through" or (when used as a prefix and not as a preposition) "thoroughly;" (for us here, it means "through"). Ager means field in Latin, and in English finds derivatives such as "agricultural" and "agrarian."  To go per agros is to go "through the fields"—like a traveller or a pilgrim.

"Beatitude" comes from the Latin beatus, meaning blessed. Related words are "beatify" and the Biblical "Beatitudes."

The phrase "never saw the darker parts of the job" is the key to finding the missing word.  This phrase indicates the correct answer will show the younger doctors were kept from the negative elements of medicine. "Coddled," meaning indulged or pampered, is the most appropriate choice.

The basic fact of the sentence is that the subject was in some way spreading "enemy propaganda," and issues of loyalty should be ignored. "Disseminating," meaning to spread and circulate, is the best choice.

There are multiple choice that could fit the sentence, but the best choice must be found.  The phrase "new techniques" indicate the pitcher created those techniques. "Innovating," meaning creating and pioneering, is the best choice.