Are fibroadenomas hard and immovable?

Not usually. Hard mobile like a marble in the tissue.
Sometimes. The typical fibroadenoma (if there is such a thing) is rubbery, round-to-oval, and movable. In contrast, cancers may feel rock-hard and immovable. However, these are generalizations and it is impossible and unreliable to differentiate a fibroadenoma from a cancer by examination alone: it is easy to be fooled.