Merge/Cut = 3D boolean. Imprint = 2D surface cut: splits the surface along the rectangle so you can pull the enclosed patch with the Surface tool. Left-drag empty space orbits.
⤢ Scale selected part
XYZ
Type an exact size and press Enter, or drag a corner (proportional) / face (1-axis) handle. With Lock ratio on, any field scales all three axes together. Scales about the part's centre.
⇅ Move surface (mm)
Enter a delta and press Enter (or Apply) to move the patch that many mm along Normal / U / V — or just drag an arrow. Ctrl+Z undoes.