Yes. The farther apart the primaries are as located in XYZ space, the larger the resulting color gamut.
This article explains how you get from three primaries to an actual color gamut - a 3D volume - in XYZ space: https://ninedegreesbelow.com/photography/xyz-rgb.html
This page has gamut outlines in LAB space for various older RGB working spaces, but doesn’t include any of the newer spaces such as the ACES color spaces and Rec.2020 : http://brucelindbloom.com/index.html?WorkingSpaceInfo.html
Such a 3D gamut viewer would be nice to have in free/libre software - is there such a thing? icc_examin has a bit of what the Lindbloom viewer had, and ArgyllCMS can generate 3D views, but I think only in LAB space, and only if the user is willing to work at the command line.
This page has some basic definitions for discussing ICC profiles, and also shows a sample printer, monitor, and camera input profile in LAB space: https://ninedegreesbelow.com/photography/pictures-of-color-spaces.html
Yes. Camera manufacturers are not usually so obliging as to just tell us what the effective primaries of their cameras are. So instead we have to make profiles for use when interpolating camera raw files, by making target chart shots to get a set of known color patches. Scanners also can be profiled starting with a scan of a target chart, if the scanner allows to disable the conversion to sRGB.
With monitors the process involves first calibrating the monitor, and then using profiling software and a color measuring device connected to the computer and monitor, which work together to send known color patches to the screen to be read by the device, which informaton is used by the profiling software to create a monitor profile.
With respect to the word “primaries” - this implies a matrix RGB profile, which is the most commonly used type of profile for cameras and monitors.