You should find most of these fixed in Version 1.1.
The UI has been changed to be (hopefully) more intuitive. The main setting to enable/disable updates is now a dropdown, and the dependent options have been changed from disabled to readonly, so that their values are retained. The core option has been changed to a select dropdown, to control the level: minor, major, or development. (Note: the way to disable minor core updates is to disable updates altogether.)
I’ve also added options to enable Plugin, Theme, and Translation updates – as well as options to disable update result emails (altogether, or by result type).
Not much I can do about the placement on Settings -> General. I think that settings page is the correct place for the Plugin’s options.