I’d have to retest in Hook 2.x re #1, but, but Hook 3, which we expect to release Sunday evening Pacific time, rounds out the commands in the search window, and I couldn’t replicate #1 in it either.
also @LucB
the current workaround I am using is to press Tab (⇥) to ‘move the focus to next window space’, from there, you can navigate up and down with ↑ ↓ (the equivalent is ⌃P ⌃N). Also you can navigate backwards forwards with ← → (equivalent is ⌃B ⌃F).