The main question is unanswerable as it couldn't happen without fundamentally changing physics in some way. However, the other one is a lot more interesting.

On a large scale, one in ten atoms vanishing would decrease both the density and mass of most objects by 10%. This would also decrease their gravity by 10%, resulting in all orbits becoming significantly more (or less) eccentric. I imagine the changes would be enough to destabilize some solar systems, potentially causing planets to perturb each other's orbits until they collide or end up being ejected from the system.

The change in density also means that gravitationally bound objects that are held up by internal pressure (like planets and stars) would collapse slightly as their internals are re-compressed to their original density. The collapse would release a lot of energy, heating up planets significantly and (just guessing here) maybe causing a burst of fusion in stars as they're temporarily compressed past their equilibrium point.

All of that is pretty bad news for life on Earth, but the worst is what happens chemically. Some molecules are just going to become different molecules when one or more of their atoms disappears. Take water, for example; a water molecule has an 8.1% chance to become a hydrogen molecule, an 8.1% chance to become a (highly reactive) hydroxide ion, and a 0.9% chance to become a (highly reactive) single oxygen atom. 18% of nitrogen and oxygen molecules in the atmosphere would also become single atoms and promptly react violently. These molecular changes would instantly kill all life on Earth (and anywhere else). There's simply no possible way for an organism to survive so many reactive molecules being introduced throughout itself. Not to mention that all DNA would be irreparably damaged from the random deletions too.

I'm sure there are some other effects that I haven't thought of, but those are definitely the most noticeable ones.