Port a Wii game to Switch

Yes, if you own the game and become an approved Nintendo developer. The rebuild happens in a normal engine project, and the console specific integration and submission happen under your Nintendo developer account because those tools are under non disclosure agreement.

Largely yes. Switch controllers have gyroscopes and accelerometers, so swings, tilts, and shakes survive. The exception is the Wii infrared pointer, which gave absolute screen position. Switch gyro aiming is relative, so pointer heavy games need a recentre button and sensitivity options, plus a stick alternative for handheld play.

Considerably. A Wii output 480p, while a Switch outputs up to 1080p docked with much more GPU capability. Higher render resolution, larger shadow maps, better texture filtering, and longer draw distance are all available without changing the geometry or animation.

Yes. Switch supports multiple controllers and can split a pair of Joy Con between two players. You still need to declare which configurations you support and handle each one, including the Pro Controller, detached and attached Joy Con, and a single Joy Con held sideways.

Yes. There is no open self publishing route to Switch. You apply to Nintendo, sign their agreements, and get access to development hardware and tools. Applications go better with a playable build and a concrete plan than with a pitch alone.