Copy measures between staves in score editor

Yes - you can highlight the notes you want to copy and hit command-C ( to copy the notes to the clipboard)

place the play head where you want it ( by option clicking on the destination staff at the position where you want to begin the insert)

hit command V - to paste the notes onto that staff.

If you are copying from one staff to another in the exact same bar positions- you can highlight and copy the source notes ( command - C)

then select the staff you want to serve as the destination - edit->paste at original position. (this does not require the placement of the playhead at the destination position) as compared to the (copy/paste option above) which only pastes at the current location of the playhead.

Just click on the staff. I have mine set to show as Red, the default is Green. You click anywhere on the staff itself ( the lines of the staff) to select it.

See example below - I used CMD-5 ( score window ) not the embedded score for this example as requested.