1. When something goes wrong,she takes care of it.
2. When something gets wrong, she takes care of it.
(Are both the same? Can we use 'gets' instead of 'goes'?)
3. When she talks, people in the studio listen to her through their headphones.
4. When she talks, people in the studio listen to her into their headphones.
(Which one is correct, #3 or #4? Are both OK?)
1 is correct; 2 is not. It's best to avoid using the word "get" or any form of it unless there's no option.
http://grammar.ccc.commnet.edu/grammar/plague.htm
See #13; even though this is referring to the past tense, the concept is there for all forms of "get" which primarily means to gain possession of something (synonyms include "bought" or "purchased" or "was given").
3 is correct; 4 is not.