Yes, when you are giving instruction to someone entitled to log the =entire= flight as PIC under the sole manipulator rule, you may also log the =entire= flight as PIC under the CFI giving instruction rule. No splitting required.
Yes, technically, the only time you are supposed to log PIC based solely on being a CFI giving instruction is when you, well, are being a CFI giving instruction, not when just going along for a ride. with a friend.
Mixed flights do happen. For example, you are going with a friend to a fly-in breakfast. The flight is 1.2. Along the way, you give him 0.6 hours of instruction for some reason. You could log the 0.6 as PIC.
I don't know if that's the kind of scenario you are talking about when you talk about splitting the time.