should add 그녀는.
No. When speaking you should almost never use 그녀. It's really unnatural.
As a trivia I'd add that the word '그녀' doesn't even exist in North Korean dialect and '그' is used for both genders there
새 秘密番號를 만들어요.
How do you know that is "She" instead of "he" or "you"
It's implied quite often in korean. Usually you would use 그 or 그분.
How would you know, specifically, that it is "she" instead of "I" or "he" or "we" etc.? What would Koreans say to indicate that a female (instead of a male) is the one making a new password?
We understand that subjects can be implied. However, if we just see the Korean sentence alone, we have no way of knowing the translation wants "she" instead of "I" or "he" or "you" or "they."