hi! I'm new and I'm a bit confused by the event going on right now? 

does any enemy in the explore thing have a chance to drop eggs? how high is the chance? or is it a special enemy that drops them? will it say in the event log if I get an egg?

I'm sure these are silly questions, I'm just a bit lost ;; 

The eggs are dropped randomly by guardians (the red monsters who are guarding treasure chests) and salamanders (the ones that look like giant lizards haha). Like I said, its random, but I would say you get around 1 egg per 4-5 islands assuming you defeat all the monsters. It definitely varies though, you might have 2 or 3 eggs on one island or not find any eggs for 10 islands. And yes, it'll say in your event log if you find one :)

you can see them in your inventory too