Oh dear that cucumber may be a problem unless it gets a positive ID, I know very little about them TBH so hopefully someone else can sort that out for you.
Nice find on the pompom but try to use patience when stocking, inverts (anemones even more so) are very fickle about water parameter swings and in a new tank it's gonna happen alot.
He should be fine though, my pompom lives in a tank with water like soup.
So finally the 'thing', if it looks like a rock and feels like a rock I would say it is quite possibly a rock.