Tommy
You are mixing right to work versus employer requirements. While the law refers to a right to pursue work and work in all EU countries without restriction, there's nothing in the law prohibiting an employer from setting requirements for a job such as nationality.
What the paragraph you pasted refers to is the freedom of movement of labour and equal right to work.
There might be various reasons for requiring nationality such as airport access, military contracts etc etc.
Again you are wrong about the language requirements. Just have a look what the ICAO approved languages are. While I agree that in a multinational company a common language must exist, this could be set to be French or Russian and not English by default. Again there is no requirements, other than ICAO English proficiency for use with ATC and thus a requirement that an employer is free to set in similar way as setting hours and experience requirements.