Once you have a project charter - which comes after the business case - the next step is to do the project planning. It is not the sponsor's job to lead that effort, rather it is the project manager's responsibility who will do C and D, as necessary. That leaves you with A as the only valid sponsor responsibility.
A project manager is identified and assigned as early in the project as is feasible, preferably while the project charter is being developed and always prior to the start of planning. The project charter can be developed by the sponsor or the project manager in collaboration with the initiating entity. This collaboration allows the project manager to have a better understanding of the project purpose, objectives, and expected benefits