What distance apart should metal stud securing brackets be placed?
Typically the studs would be fastened to the wall with clips or L metal.
Spacing would be 24 inches vertical &amp; 48 inches Horizontally.
Metal studs have a punch out for bridging typical 4' 6" vertical for cold rolled channel to be in stalled some bridging require clips screw attached and others just snap in place depending on the manufacture.
You also need to check on the Seismic rating as you stated plaster was being installed.