I copied a bone from one model and I pasted it to another model, however I don’t see any animations. Is there a way to copy its animations as well?
sure thing.
a) Given that you already placed the bone in the same hierarchy under the same (root) or top center of gravity bone:
Select your original animated bone, open an Graph editor view. in the 3d viewport change to POSE mode. Select the channel curves (the bone name Scale, transform, rotate) on the graph editor, and COPY.
Switch to the bone that doesn’t contain the animation (but was copied) and on the 3D viewport press "i, then press “o” (letter), to insert a blank keyframe for rotation and translation.
In your graph editor, you’ll see new keyframes have been set on the current frame number.
Hover your Graph editor, and with the keys already selected and the playhead on the frame number you need to use (generally paste on frame 1), press CTRL+V to paste.
Your bone animation should be pasted.