For the first issue there is an easy fix. If you long tap on the (I guess two, since you lost one screen) dots above the home button you can choose between apps and widgets. Since accidentally removing one app on a screen with many apps doesn’t remove the screen I guess you removed the “My Apps” widget. So tap on widgets swipe till you find the my apps widget, long tap it, “move” it to the right edge of the screen until a new screen appears and then release it.
Issues 2, 3 and 5 are probably resolved by removing the screen protection foil, which is only meant to prevent scratches during transportation and shoul be removed before first use.
If you continue to have a black screen during calling try the workaroubds from this thread: