Restarting init without restarting the system

For the second question, the answer is no and you should have a look at Resources for portable shell programming.

As for the first part - first of all, you certainly have to be careful. I'd say perform several tests to make sure - because the fact that someone does have systemd (for ex.) installed, does not mean it is actually used as the default init. Also, looking at /proc/1/comm can be misleading, because some installations of various init programs can automatically make /sbin/init a symlink hardlink or even a renamed version of their main program.

Maybe the most useful thing could be to look at the init scripts type - because those are what you'll actually be creating, no matter what runs them.

As a side note, you might also have a look at OpenRC which aims to provide a structure of init scripts that is compatible with both Linux and BSD systems.

On Debian the following packages use /run/initctl: systemd, libvirt, sysvinit, refpolicy, gradm2. (from https://codesearch.debian.net/ ).

I think it is the normal way to tell init to change runlevel.