As workplaces becoming increasingly competitive nowadays
"are becoming" or simply "become"
Workplace is distinctly different from school which success is measured by qualifications.
which success? school success? probably "At the workplace the better your qualifications are, the more success you can achieve, which is different from school" or smth like that
But it is clearly not the case at work where teamwork is required for large project that are nearly impossible to be done by individuals. Despite these projects, cooperation is often needed in daily works as well.
Switch the sentences to add more logical connections. "But it is clearly not the case at work where there is a need in cooperation for everyday job as well as for large single projects"
Only when everyone in the firm is working in the same direction can the highest effectiveness be achieved.
Not sure about word order, sounds a bit wierd...
You could say "The firm can achieve its highest effectiveness only when everyone is working in the same direction."
However, try to avoid the same constructions.
it is unlikely that the highest workplace effectiveness could be achieved . Only when everyone in the firm is working in the same direction can the highest effectiveness be achieved .