I just started the Ebilia egg hunt, and I've been searching the little explore screen for them for about 15 minutes now, without a single find. Not even an item. So, I went to the species list, and saw that Ebilia still says 0%, even though it also says the hunt is now active? Am I missing something, or is this a really annoying bug?

No it just takes time for you to find eggs in the cave.
tle="" target="" style="font-weight: bold;">http://www.rescreatu.com/forum/cat/general/helpandfaq/-unofficial-incomplete-event-searching-guide/~page/1/

Check out this guide to also make sure everything you're doing is the same.