Projects exist within the context of an existing organizational structure, are managed through delegated authority, and should not be run like independent fiefdoms. All of your sub-questions boil down to an organizational failure to properly charter the project and define the project manager's scope of authority (if any).
In addition to the process failures, you appear to lack influence with both your management team and with your project members. Regardless of the reasons for this, you must either fix the problems (if you can) or leave the project. Your project is unlikely to succeed under the status quo.
Regardless of framework, all projects require some sort of inception document. This is usually called the project charter. A good project charter should also define the roles for the project, including:
- project sponsors,
- technical decision makers, and
- lines of authority.
The project manager is often not a manager or authority figure in the traditional sense, and on some projects may have responsibilities without delegated personnel or budgetary authority. This is an organizational decision, and one which your current organization has either not made, or has made in a way that you don't agree with.
Authority Must Be Delegated
Authority must always be delegated from the top of an organization. This delegation is often a chain where the project manager derives whatever authority he has (if any) from the project charter or project sponsor.
If you have not been granted any authority, then you must use influence rather than a command-and-control style to manage your projects. Based on your description, it seems as though you currently lack both authority and influence. You may want to discuss these issues with the person you report to.
Who Works for Whom
You work for the company, and any authority you have is delegated from senior management. Therefore, when you ask:
[W]hat if CEO intervenes and countermands your decisions?
it seems likely that one or more of the following statements are true:
- You are making decisions outside the scope of your delegated authority.
- You are making decisions that are out of step with your organizational norms or the management team's expectations.
- You do not have the appropriate levels of trust and two-way communication between you and your management team.
- You are at odds with your management team.
- You do not understand the organizational chart or the source of your delegated authority (if any).
While it's often preferable for the senior management team to work through a project's appointed leadership to manage a project, it is certainly not required. Regardless of how you feel about their decisions, it is always up to senior management to determine how they want a project or team to be run.
If you find that your style of project management is a poor fit for your organization, or that you lack the influence or finesse to manage the political aspects of the project, then you may want to consider looking for a different role within your company—or even trying to find another company where your project management style would be a better fit for the company culture.
The only real power you have that is not delegated to you is the right to "vote with your feet." Fix the process if you can, fix your attitude if you can't...or just move on. Good luck!