First, you want to ask yourself what charisma means; think about both the definition as you know it and the part of speech.

so say you know this much: charisma means something along the lines of “charm” and it’s a noun.

1. Most people seemed to respond to the candidate’s CHARM rather than to his political agenda.

this sentence works with your synonym plugged in. people liked the candidate’s personality more than the candidate’s plans for policy.

2.Benjamin was overwhelmed by his co-worker’s CHARM, and he promised to repay him as soon as possible.

this one still works. benjamin is floored by his coworker’s charm and promises to repay him.

3.Alyssa’s acting talent was not great, but she hoped her CHARM would secure her a role in the play.

this works. alyssa is hoping that her charm is enough to get her a role in the play, even though she wasn’t the best actor.

4.Though Farhan could be charming, he knew that he could not rely on his CHARM to get the job.

so, given that this sentence used charming as a context clue for the definition of charisma, it’s definitely used correctly here. farhan is charming, but he knows he can’t just bank on that getting him through.

5.Julio used his CHARM to haul the leaky boat and its soggy passengers out of the water.
“charm” wouldn’t be much use here. julio needs strength and strategy to save passengers from a messed up boat–a smile and a wink wouldn’t really help him. this is the only sentence that uses charisma incorrectly.