Listview and checkboxes - setting, checking, getting checked

I'm having an issue with checkboxes on a listview, checking items, and listing just those checked items. This is my first android app, and without knowing what all is needed here in the way of code to help figure it out, I have recreated the problem in a bare-bones app that demonstrates what is going on. I suspect it is in the getView() method, but I'm not really sure.

Problem One: When more items are in the list than are visible, checking items at the top of the list also checks items that are not visible.

Problem Two: In the onOptionsItemSelected method there are two ways I've tried to get just the checked items. One is currently commented out, but they both fail in different ways. There are comments above each method that expalins what goes wrong.

http://ift.tt/1toKWbH