this case is unneeded because no enumeration value can possibly correspond to it

* Removed use of raw QTimer* pointer.
* Update to use type-safe QObject::connect.
* getKeyName can be a static local function.
* Prefer to use function arguments instead of member variables.
* Store Qt::Key instead of converting string back into keycode.

This makes clang-format useful on those.

Also add a bunch of forgotten transitive includes, which otherwise
prevented compilation.