You are talking about two separate problems, so I'll answer them separately.
There is no system-wide setting for screen sensitivity. Like Joe mentions, it is app specific (even the Start Screen is an app), and the developer can do a couple things to change it. I talk about the GestureListeners in a comment on Joe's answer, but the other is a common mistake developers make and is simple to fix.
12px margin, yep, a margin...The margin is not just a visually pleasing guideline but is a functional one as well. If a developer doesn't stay 12px away from the edge of the screen, the gestureListener will see a swipe gesture when the user is just trying to hold the phone and read. Or they may be switching hands, so the slide of the skin across the edge will be interpreted as a swipe. You could ask the developer to increase their margins and that will cut down on unintended gestures.
The second question comment you mention is about when you go back to where you were after an unintended swipe, you have lost your page position. I agree, that is extremely annoying, but there has been a fix for that for a while. The developer should be saving page state when navigating away, I do it in my apps and consider it a must. There is a lot of documentation available for that feature and you could let the developers know they need to add it in the app (especially a big name like eBay).