I think that both of my problems are now fixed.
I gently pressed down on the plastic paddle (using a cue-tip) below the spring under the end key, and it now reacts normally. It seems like it was stuck up just a little to high, which caused it to register a stroke anytime the key was even slightly pressed.
The pause key problem has gone away after pressing it about a hundred times repeatedly, until no strangeness is reported in Aquatest. My fingers are crossed on that one.