I suppose there's only one moon then? 

I think global events, if agreed upon by everyone, could definitely occur. They'd certainly spice up things.
Eclipses repeat in a region every few decades, I think. 
I'd surmise the current map isn't much bigger than North America, so a solar eclipse would probably be at least somewhat visible over a large part of it, although the total eclipse would only be seen in a much smaller section.

I guess we could discuss about climate change, such as ice ages, or smaller events like droughts, floods, etc. There's no reason we couldn't.