I have keys but no locks. I have space but no room. You can enter, but can’t go outside

I resemble a bat, but I do not fly. You can share me when water falls out of the sky.

Born from puncturing pain, I remain, Like living art, but not on a page. I sting to arrive, yet forever I stay, A memory carved in a colorful way.

I have paws but no feet, I shoot beams of light but am not superman. I can move backwards and forwards in time, but I am no time machine.

I can run, but I cannot move. People use me to chill foods.