There's no good answer here, I believe. As we've seen, a ritual can be done entirely in your head, which would make no sound whatsoever.
The more important question would be, how does the caster see it? Has he been taught to chant an ancient song to gather power? Or stomp their feet in a steady rhythm? Would the desired effect make it reasonable to have something loud or otherwise overt while casting the spell? Do they usually have to do certain gestures? Draw something? And so on.
I guess what I'm trying to say is that yes, it is possible, given the right circumstances. If you are trying to keep all those things in your head only, so nobody around you notices them, that's going to make the spell all the more difficult. And if you start to imagine the things in your head, people around you might notice you concentration, even if they don't know what exactly you are doing.
So for case (1), it should not be a problem, as long as the casters style provides it. If it doesn't, I would require a description or an aspect as to what he's doing different in that situation, so nobody notices.
Case (2) is a lot harder. You not only have to cast the spell, but you have to use the components for the spell, too. It all comes down to "can you describe to me how you are doing that without anyone noticing", I think. If you are sitting in a busy restaurant and want to cast something, doodling on your napkin could account for some ritual components, and few people would see anything other than some doodles.