The external monitor problem is probably a well-known gdm3 bug: gdm3 with nvidia modeset=1 stops the nvidia driver from detecting external monitors (possibly it invokes some wayland features when it shouldn't). It is not a problem with nvidia-prime or with the kernel. You can fix it by using lightdm instead of gdm3. This bug affects fedora as well.
ubuntu 19.04 has reverted to nvidia modeset = 0 be default to avoid this bug (at the cost of unfixable screen tearing for Optimus users in nvidia mode).
nvidia-prime does always include the nvidia modules in the initramfs kernel, this was a change in 18.10 backported to 18.04. Previous nvidia-prime pacakges used to rebuild initramfs to add or remove the module, but this is not required any longer. Choosing prime-select intel means the nvidia module is unloaded when the machine is starting.
The external monitor problem is probably a well-known gdm3 bug: gdm3 with nvidia modeset=1 stops the nvidia driver from detecting external monitors (possibly it invokes some wayland features when it shouldn't). It is not a problem with nvidia-prime or with the kernel. You can fix it by using lightdm instead of gdm3. This bug affects fedora as well.
ubuntu 19.04 has reverted to nvidia modeset = 0 be default to avoid this bug (at the cost of unfixable screen tearing for Optimus users in nvidia mode).
nvidia-prime does always include the nvidia modules in the initramfs kernel, this was a change in 18.10 backported to 18.04. Previous nvidia-prime pacakges used to rebuild initramfs to add or remove the module, but this is not required any longer. Choosing prime-select intel means the nvidia module is unloaded when the machine is starting.