I can't help with your templates as they all vary and I don't use wordpress or anything like that but they will all have some mechanism to allow you to enter new code and new styles.
As far as responsive goes then you will need to build that into place. A flyout menu isn't really something that would normally fit into a responsive site as you can't really control the width easily at smaller window sizes. A flyout menu should revert to a normal menu at small screen sizes but that has to be designed from the ground up using media queries.
If you have a responsive site then you should probably go with something simpler and more manageable. The use of flyout menus is usually the sigh of an ill thought out menu structure in a site unless there are good reasons for it.