Brew Services vs Launchctl – How Brew Services Differ from Launchctl Services on macOS

That isn't actually launchctl creating a new process; it's most likely dnsmasq itself. If it fork()s into the background, launchd can't tell; then when it talks to launchd, launchd creates an anonymous entry for it. Make sure dnsmasq doesn't background itself.

(The - listed for the regular launchctl list output indicates that the original dnsmasq process exited.)

that note just refers to the 4 libraries gmp, mpfr, libmpc, ppl and I think means that if you use these they need to be before the standard search path.

Your issue is where is the compiler looking for standard library headers (and later libraries). gcc defaults to /usr/include which is installed for Apple's compilers and that gets redirected by version to the path you see.

You need to explicitly set the paths to look in the hombrew compilers path first