For starters it would help if you give a general area where your items were found. When looking at the item in the second photo, that's in your left (right side) hand, it looks like a small fossil sea urchin. Not sure of the other one in the second photo. The one in the first photo is also a fossil sea urchin.
The first one is indeed an echinoid (sea urchin) fossil. In the second picture, the item on the left is unidentifiable (perhaps coralline or some kind of reef encrustation), but the item on the right is a fossil "button coral". Don't see those too often, so that's a nice find.
These are typical forms for button corals (these aren't from your locality):
The first picture is an Echinoid. From that region it could either be ECHINOCORYS TENUITUBERCULATUS or ECHINOCORYS VULGARIS (I am guessing it is the latter). Nice find!