The “Air. Design.” comes from BM Slider. Edit homepage, you can disable BM Slide.
What’s kind of static image you want? like it? -> http://www.uiueux.com/wp/air/home4/ (it is a slider, do you want only one?)
There is only “default demo” in Air theme. Please go to Appearance > Theme Options > Font Settings, if there is not fonts in selector, please click the “Update to new Google Font Data” button, it’ll load the latest fonts from Google’s servers.