Under doesn't make sense in either sentence. The way your first example reads is that "QA system" is some kind of image, and that there is supposed to be a background image appearing below it, but it doesn't show up. But since a QA system is not an image, that doesn't make any sense. In doesn't really work either. It doesn't make sense to be missing an image in a system. You can be missing an image on the QA screen or on the QA page. I can't 100% determine what you're trying to say here, even after reading comments on the question. But maybe you mean something like this:
The background image is missing on the QA page.
This means that in your application there is a page dedicated to QA, and this page's background image has failed to load.
Your second question is pretty different; I know both are re: "in vs under", but since neither in nor under make sense in the first case, it's not really the same. Regardless, the correct word to use with weather is in:
I wouldn't jog in this weather.
We go out in the rain and out in bad weather. Once you're outside, you're in whatever type of inclement weather there is. Under doesn't make sense. You aren't under rain, for example; the rain is falling all around you. You're in the midst of it.