Strainer comes before the RPZ, and yes, you can get an RPZ with a brass strainer already installed on it. Personally, if I had to have a strainer, I'd special-order one with a 100 mesh screen, and really protect the RPZ (and sprinkler system, too) from any debris.
Air gaps are for connections to a drain line, and you don't have a drain line when an RPZ is installed outdoors.