Yes, that device will work for the PC.
But you still need a router if you have more than one device.
The modem hands out one and only one IP address.Either to a router, or to the PC. The router then hands out multiple internal IP addresses to all your devices, either wired or wireless.
Yes, you can, via ICS, retransmit from the PC to the other devices.
But there is no difference in wiring if all the other things are wireless. Just have them connect to the router.
Using the PC as the hotspot, it has to be on for anything else to connect. I would just use the router for what it is designed for. No more or less 'wiring' than using the PC as a pseudo router.