LEED v4 CxA

The CxA may be a qualified employee of the owner, an independent consultant, or an employee of the design or construction firm who is not part of the project’s design or construction team, or a disinterested subcontractor of the design or construction team. In your case, I consider that assigning the Fundamental Commissioning tasks to an employee of the construction firm who is NOT part of the overall project's team would be ok.

Yes, if the construction firm is the owner, then the CxA can come from that organization. The ownership should be confirmed by contract. If it is a DB contract that is build-to-suit and ownership changes at the end of construction, then it is not as clear that they are truly the owner. If they are developing the project and then will operate the building with multiple tenants, then they would be the owner for sure. There are some contracts where the GSA is the only occupant but it is a long term lease back to a contractor/owner/developer. In this case, and this is really my opinion, the contractor can hold the contract for the CxA, but that CxA should be an independent firm.