I'm wondering what would be the most efficient way to copy the structures/hight differences from the surface of the first picture to the bottom surface of it. I should have used a mirror from the beginning but didn't think of it :( is there any way to still do it efficiently now?
Enter Edit Mode and select the faces you want to mirror. Press P and choose Selection to split the faces into a new object.
You can then apply a Mirror Modifier to the new object.
Remove the X axis toggle and apply the Z axis instead:
At this point the new object will be mirrored around its point of origin, which it inherits from its original object. This might be in the wrong position and your mirror may be in the wrong place like this:
You can fix this by updating the objects Origin. The easiest way to do this is to first select the Parent object. Press Ctrl + Alt + Shift + C and select Origin to Geometry:
Next, with the parent object still selected, press Shift + S and choose Cursor to Selected.
Next select the Mirrored part and press Ctrl + Alt + Shift + C and select Origin to 3D Cursor. This will set the Origin for the Mirrored part to the same position as it's parent part and your mirrored mesh should appear in the right place: