Regarding the use of “they” meaning “him/her” or “their” meaning “his/her”. Most publications guard against sexist language.
This sentence is sexist: “A man who applies to be a nuclear scientist is testing his limits.” It’s sexist because men or women can apply.
So, to be non-sexist, you might write: “A man or woman who applies to be a nuclear scientist is testing his or her limits.” It’s non-sexist, but it’s also awkward.
It may be better to write: “A man or woman who applies to be a nuclear scientist is testing their limits.” “Their” is easier than the awkward expressions “his/her” and “they” easier than “him or her”.
Strictly speaking however, this is grammatically wrong in this the Third Millennium. But it’s becoming common and soon the rules of grammar will change and declare it correct simply because so many writers now do it. The recent Third Edition of The Macquarie Dictionary says the use of their for his or her to provide a gender-neutral possessive pronoun is part of our evolving language.