I can be shuffled, picked, passed around, and answered out loud. What am I?

I help mistakes disappear, but I make crumbs when I work. What am I?

What hat helps a group think, even when nobody wears it?

What mountain can fit in your pocket but is too sharp to climb?

I make people move, but I never touch them. What am I?

What pencil never writes, no matter how sharp it is?

I get shorter every time I do my best work. What am I?

What fire can cool tempers instead of heating them?

What key opens a song but not a door?