I can't help you very much, I'm just a 2nd year microbiology student who happened to have a lab about gram positive cocci (isolated from the skin, such as Staphyloccus epidermidis and Micrococcus luteus) recently. I haven't followed your other posts, sorry.
Motility in cocci is very rare (unless they are very ovoid rods and not cocci). The bacterial shape by itself isn't very efficient for motility; for the opposite reasons, spirilli are very frequently motile.
At that size, it is most likely bacteria.
Interesting that you use gelatin. I guess that's a lot less expensive than agar.
A catalase test is not that useful; most organisms are cat +. It can be useful to distinguish Staph. for instance which is cat -.
I didn't even know that you could distinguish the gram-type with an optical microscope just like that, but the microcoscopes we use only have a 1000x zoom.
I don't know anything about that "small red marble", never heard of anything like that.