1) If you use the image as the bg image for the slider + background size “cover” you need to understand that image will be cropped on different devices because background-size “cover” works in this way https://cssreference.io/property/background-size/
You can change background position – http://prntscr.com/n6xfby (will be applied for desktop and mobile) for example http://prntscr.com/n6xg18 > https://prnt.sc/n6xggu
2) Theme Options > Header > Mobile header > Promo popup in mobile menu > Off. Also, you can disable the Newsletter (Promo popup) at all via Theme Options > Promo Popup > Enable promo popup > Off.
3) Theme Options > Typography > Menu > Menu 1 level (hover, active) > Select color.