It's a bit hard to tell from the piccy but it probably is some kind of sponge. The green shiny ball in the piccy is bubble algae, best if you remove this as it will spread and become a bother. Don't pop it whilst it's still in your tank otherwise the spores will spread. Best thing to do is next time you do a water change place the whole rock into your bucket of removed tank water then gently ease it from the rock with tweezers or if its quite big you'll be able to do it with your fingers.
The white thing is definately sponge. I get it a lot in my tank usually just inside the rock crevices or the cave entrance. It's fine though, it won't cause any problems for you. Have fun discovering...I do