You might want to change the size of the background image to fit the whole screen. In my case, there is a grey strip on the right side of the screen.
To automaticly reset the player when falling, you could check if the y coordinate is either lower than 0 or higher than the screen height, depending on the origin of 0,0. In the same process, you could solve it for when you get shoved out the left side of the screen.
Something that could be fun too would be if there might sometimes be two platforms ontop of eachother