Here is one way to answer the two multiple choice questions.
Here is the first one.
Many parents today believe that youth of today are very liberal and curious. Even though some of them are Catholics, each of them claims that "It is okay to let our sons bring condoms...for emergency. Every liberal and concerned mother has this kind of thought."
However, no one is "attacking the character, motive, or other attribute of the person making the argument" which is part of Wikipedia's description of this fallacy.
However, no one "appeals to force or the threat of force to bring about the acceptance of a conclusion". This doesn't fit Wikipedia's description of the argument.
The phrase "misuse of authority" sounds like it refers to "argument from authority" where "a claimed authority's support is used as evidence for an argument's conclusion". That authority would be the "liberal and concerned mother". This appears to be the best choice.
This sounds like the "ad nauseum" argument style where the "question has been discussed extensively, and that those involved in the discussion have grown tired of it". However, there is no evident repetition in the argument.
Here is the second.
In a certain discussion among local executives concerning poverty in each respective area, one of them said that "Friends, we have to design a program that will alleviate the life condition of the marginalized constituents."
I couldn't find an alternate name for this supposed fallacy, but then I also couldn't find any obvious jargon in the argument. However, the phrases "marginalized constituents" and "life condition" seem like an odd way of speaking.
Wikipedia describes this as speech where "inappropriate, invented, or nonsense words are used to give the appearance of knowledge and so confuse or amuse the audience". However, I didn't find anything particularly confusing about the argument. As the OP suggests perhaps there is an underlying motive involved.
Wikipedia describes an association fallacy as "an informal inductive fallacy of the hasty-generalization or red-herring type and which asserts, by irrelevant association and often by appeal to emotion, that qualities of one thing are inherently qualities of another." There might be an appeal to emotion here which suggests that the next option is better than this one.
Wikipedia describes this as "the manipulation of the recipient's emotions in order to win an argument, especially in the absence of factual evidence." The use of "marginalized" without further argument about what the "program" involves seems to encourage the listeners to accept whatever program is offered without looking at it closer. This appears to be the best choice.
"Ad hominem", Wikipedia https://en.wikipedia.org/wiki/Ad_hominem
"Ad nauseum", Wikipedia https://en.wikipedia.org/wiki/Ad_nauseam
"Argument from authority", Wikipedia https://en.wikipedia.org/wiki/Argument_from_authority
"Appeal to emotion", Wikipedia https://en.wikipedia.org/wiki/Appeal_to_emotion
"Argumentum ad baculum", Wikipedia https://en.wikipedia.org/wiki/Argumentum_ad_baculum
"Association fallacy", Wikipedia https://en.wikipedia.org/wiki/Association_fallacy
"Double talk", Wikipedia https://en.wikipedia.org/wiki/Double-talk