Well, maybe you did something wrong in CSS when you was changing the menu. However, the problems you have now are not related to the menu.
Our templates looks ok on mobiles out of the box. But, when you develop and add content, you always must have responsive features in mind. The changes that you made in template makes problems on mobile devices.
I don't know what exactly you'd like to change on mobile output, so I can't give you exact answers.
Thanks
