How can I resize such items without changing the curvature at edges? You know, I don’t want the half-circles at the extremes to become half-elipses.
Hold down the shift key while dragging a corner handle.
Or, the more accurate and flexible method is directly selecting all the vector point anchors for one side (2 corners) and dragging that over, then selecting the other half to drag another side in another direction to achieve the desired dimensions.
You can only do that with the “Direct Selection Tool” which is the second, white, “pointer” button in the Illustrator tools palette. It selects points of a shape instead of the whole shape.