Discussion 1: A project is always time-sensitive. Every organization expects the

Discussion 1:
A project is always time-sensitive. Every organization expects the deployment within the given time maintaining high performance.
The organizations also concentrate on the money spent on a project dividing it between the resources and the phases being used.
The project management life cycle has six phases:
Intake, Initiation, Planning, Execution, Control and Closure.
Intake includes project proposals, review and approvals.
In Initiation phase a project manager is assigned to the approved proposal and he gathers the business requirements.
Plan phase concentrates on recruiting project team members and develop a plan for the implementation through project meetings and discussions.
Execution phase is to implement the tasks planned in plan phase and perform phase gate review.
Control and Closure phase is to prepare closing notes, create closure documents, archive project artifacts. In this phase, monitoring is also done to troubleshoot project issues.
Project Budget depends on how many resources are utilized for it.
The more number of phases, the more number of resources are considered to be involved.
Each additional phase also increases the expected completion time of a project.
Sometimes, not all EPM phases are required for a project. Taking into account the requirements of the project and developing a stable plan would help saving time and money and would also result in a successful project implementation.
References:
Newman, William D. (2014). Financial Planning and Analysis Using SAP EPM.
Bardoliwalla, Nenshad, Buscemi, Stephanie, and Broady, Denise. (2011) Driven to Perform.
Discussion 2:
A PMO usually acts on behalf of the business organization to manage a group of projects for the business but those projects are typically executed inside of the IT organization. The PMO is the source of documentation, guidance and metrics on the best practice of project management and execution. For that reason, it is typical for a PMO to exist in inside of the IT organization but, in certainty, they take direction from the professional sponsors that they support.
If the projects are mostly computer associated including software or hardware, programming, operations, and other IT tasks, it should fall under and reporting to the IT department or IT division of a company.
If the projects are associated more on development, Infrastructures, modernization, building or maintenance. it should come under the engineering division or the PMO can have its own separate depending on associated cost and budget.
Another noteworthy factor is that the role of a PMO is changing quickly as a result of Agile environment, instead of focusing on management and control of projects, the role of the PMO is shifting to more of an assistance and support role. So, In an Agile environment, it’s kind of a doubtful point of to whom PMO should report.
From my viewpoint, Yes, it is acceptable that the PMO reports to the chief operation officer. The PMO is made up of highly experienced project managers who will be leading multiple projects and projects teams that also consist of personnel from all different departments. For the Project to work, it is important that PMO is managed by C level management and executives to remove all obstacles and make executive decisions for the project management team. 
References
1.  Giraudo, L. & Monaldi, E (May 11, 2015). “PMO Evolution”. Project Management Institute. Retrieved May 6, 2018.
2.  Eric John Darling; Stephen Jonathan Whitty (August 2015). “The project management office: it’s just not what it used to be”. International Journal of Managing Projects in Business. Emerald Publishing