paparazzi (freelance photographers who sell photographs of celebrities to the media)

sugar daddy (a middle-aged man who pays a more younger girl in exchange of her companion)

celebrity; star; famous person

chase, run after

Alternative form of 追い掛ける

private

private life; personal affairs

(childish) papa, father / (slang) prostitutional customer

question, problem on homework etc. / a question; a matter (of time etc.) / a problem (something that needs to be dealt with); a trouble / an issue; a matter

(と〜) thinking that […] (with the next clause explaining that the truth is contrary to expectations)