1) She has mastered the English language.
- 'She has mastered' is the present perfect used for past experience up to the present. It suggests learning English is something she started in the past and continues to improve at, until she masters it in the present
2) With valuable insight into how to work with people
- this sounds a lot better. 'Insight into' is a more common collocation and a short clear statement - we like those in English.
3) Anyone (could) take pride in being so single-minded as she.*
- This is better, this is a negative statement about a person. Could is better because it suggests anyone is able to, but may not take pride in being single minded would suggest everyone is the same.