In which process is a project manager identified and given the authority to apply resources to project activities?

The following is a network diagram for a project.

What is the critical path for the project?

A project manager has received a new request to integrate more features to a product. The team is fully allocated, and there is no budget to acquire new resources.
What strategy should the project manager implement to deal with this situation?

Management wants to be sure that the project is following defined quality standards. Which of the following should they look at?

A product company is transforming the way it develops and releases products in the market Executives believe that this is a high-risk initiative, and this initiative must be successful What should the project manager do in this scenario?