Humans could, if we (as a species) could all work towards survival, the most powerful feature we have evolved is the intelligence to adapt rapidly within lifetimes rather than over millennia.

I'd like to think most countries would band together to be able to survive a sudden event as all of their survival is dependant on it.

I'd say most species couldn't adapt before a sudden event (how would they know?) but can adapt to the after effects of such event.

Yes most species, but they are rather small. If you want to see tough then have a look at what Bacteria and Archea can survive.