The only bad thing I see is that aiptasia at the top of the rocks in that one picture.. something everyone deals with though.
As far as feathery things and spongey ball things, they are probably exactly that, Featherdusters and sponges, both are good to have in the tank and are filter feeders helping to clean the water. The small featherdusters that come on live rock usually have a 1/4"-1/2" tube and a feather thing coming out the end of the tube. They are actually worms with a feather thing on their head to collect stuff in the water.. sponges come in all shapes, colors, and sizes, but that ball sponge you have is one of the most common ones I see in an aquarium. Good to have.. no worries.