Since it seems to have been one-off events, chances are, someone just "aimed" badly while standing at the toilet. I wouldn't jump to conclusions. Wax rings don't typically wear out. As long as you don't disturb them, they're good for the duration.

I thought I had this same problem once, but it turned out to be occasional condensation on the cold ceramic bowl....

Keep an eye on it. I have seen the rings leak on certain times and not others. Like if a large deposit has been made causing the water to drain slowly.

Second issue - my toilet is rocking back and forth...do we need to reset it with a new wax ring?

Yes, but first find out why it is rocking. If it is simply loose, tighten it down with a new wax ring. If it is rocking because the pipe flange is too high then the flange has to be reduced to allow the toilet to sit on the floor.

as hendricus has said, tighten it up, if thefloor is not leval and it still rocks, i have used plaster of paris
to 'caulk' around the base of the toilet
when it hardens the rock will go away. it will also
not stick to the tile and ruin it as grout will do
BUT...do this ONLY if the toilet is not leaking

Thanks for the answers to the original question. I don't think it was a "aiming" issue, but the other 2 ideas could be right. I will keep an eye on it for now.

There are some water closet that have a weep hole under the bowl. When they make water closets they just kind of plug this, sometimes they leak, also if your wc rocks check the bolts to the tank. When you install a wc you should shim the back as needed, never the front.