The MSI mainboard and the Razer laptop are both USB HOSTS. The connection between two USB link "partners" can be only if one is HOST, and the other is DEVICE.
The Type-C USB specifications do define so-called DRD - Dual Role Data ports, which can turn itself into being a host or device. However, to have such dual-role functionality from a PC, the system must have TWO USB controllers inside, one acting as xHCI-compliant HOST, and another IP (piece of silicon) that can act as USB device (with all necessary attributes as USB class etc.) The external Type-C port then is internally multiplexed into xHCI or DCI hardware block depending on cable identification rules. The mainstream desktop systems do not have this functionality designed in, but all Intel systems that targeted "mobile space" (Atom line of SoC) usually do have this dual-role functionality.
So the answer to the first question is: yes, you can try to connect both systems with C-C cable, but chances of data transfer are slim, unless the one of systems clearly identifies itself as Dual-Role system (aka "OTG") in its datasheet.
Even if a silicon hardware does have this internal USB capability, the system must provide proper handling of Type-C CC (communication) channel, to determine the role of ports, and engage proper software stack. The Type-C port must be designed in a way that no VBUS power is applied until a cable is plugged in, and both ports sort their identities out. Host ports have CC pull-ups, while device ports have 5.1k pull-down on their CC pin. If both ports have the same "gender role", VBUS power shouldn't be turned on. So the answer to the second question is - if both systems are USB-IF certified, there should be no concern of VBUS power collision.
The answer to the third question is negative, there is no need in any "crossover cable", all crossover is handled in muxes behind the Type-C connector. If both ports are DRP, they will periodically advertise their identity, and the result will be selected at random