The Search Everywhere (Shift-Shift) window disappears when I switch to another window. So it is impossible to copy information from the Search Everywhere window to another document. It also cannot be pinned or docked.
I would suggest the same behaviour as with the Find in Path window, that remains visible when loosing focus.
Also: I miss the Recent Searches in the Search Everywhere window.
IntelliJ IDEA 2017.2.6
Build #IU-172.4574.11, built on November 13, 2017
JRE: 1.8.0_152-release-915-b12 x86_64
JVM: OpenJDK 64-Bit Server VM by JetBrains s.r.o
Mac OS X 10.11.6