Graphiola of palms
Looks like a fungus very common to palms that is attracting other insects and those white dots are eggs.
What kind of soil did you use? Do those pots have drainage holes?
Edit: This is another good article about palm diseases. This might be scale, but I doubt it at the moment. This article discusses fungal spots that grow through the leaf and can be scratched off...
common diseases of indoor palms
The white dots on your rubber tree plant are eggs. Don't know which insect laid them but I'll be you can find it in the rocks on top of your soil. I'd clean that off the surface for sure. Did you use potting soil or did you use garden soil? Is there a hole at the bottom of these pots? Have you fertilized?
Do not allow your cat to munch on the rubber tree plant. Your cat needs some kitty greens you grow on your window sill. Is your cat indoors only? Take scissors and cut a new point on your leaves.
I just need a bit more information to solve this...thanks!