1. If you mean one manager, this requires an article. The manager's job is not easy. This manager's job is not easy. In general, a manager's job is not easy. Simply "manager's job [should be singular] is [singular]" is not correct. Manager's jobs are -- not correct.
2. Better: I'm applying for a manager's position. I'm applying for a job as manager.
That's fine, but for me feels less specific. If there is a specific job that is being advertised, I'd use my version. If the company is accepting resumes in general for positions that may be open now or come open later, I'd use your version.