1. The dog is playing with her.
You need to use the pronoun her because it is the object of this sentence. The pronoun she can only be used as the subject of a particular sentence, and in this one, we can see that the subject is the dog, therefore, it cannot be her. So instead, you should use the object pronoun, which is her.
2. The librarian asked my sister and him if they would talk more quietly.
The explanation for this example is the same - since the boy is the object of the sentence (along with my sister), you need to use the objective pronoun, which is him. The pronoun he is used as a subject of a sentence, and we can see that the subject here is the librarian, so it cannot be the boy.
3. a. generosity = 5. largesse
The word largesse comes from Latin largus, which means copious, abundant, a lot of something. So when the word was implemented into English during the Middle Ages, it got the meaning of generosity - of giving money and gifts to others, helping them, etc.
b. talkative = 4. voluble
The word voluble also comes from Latin (like many English words), and it meant to roll, to rotate. When implemented into English, it gained the meaning of someone talkative, a person who is either talking fluently (which is a positive thing), or incessantly, without stopping (which is usually a negative thing).
c. conflicting = 7. discordant
The word discordant is derived from the word discord, which means a disagreement, a conflict, a fight, hostility, strife, etc. So by extension, a discordant person is someone who is causing conflict, who likes fighting with others and making problems.
d. appealing to = 6. invocation
This isn't exactly what invocation actually is, but it is the closest meaning among the options above. When you invoke someone or something, it means that you are calling them, referring to them, mentioning them. So an invocation is an acknowledgment of a particular person or a thing, or something/someone you are appealing to.
e. having more than one mate at a time = 3. polygamous
The word polygamous comes from Greek, where poly- means a lot of, much, and -gamous refers to marriage. So when translated, polygamous literally means 'married to more than one person.' Nowadays, this doesn't only refer to marriage, but rather romantic relationships in general - if you are dating more than one person at the same time (and they are all aware of this and okay with it), then you are a polygamous person.
