Is it ok to use drop-down menus in a Mobile Website which opens on clicking? Like http://ux.stackexchange.com
I don't think there is a simple answer here. Some of the pro's and con's that you need to think through to decide on the subjective issue of what is best for your application are:
That said there are many applications where it does make sense to use them, the most common probably being the Safari browser taskbar.
As a general rule though I would avoid using them unless absolutely necessary. Too often they are taken as an easy way out of a UX problem when there are better solutions.
Sure you can use one. I think the best way to use a drop down menu on mobile is to expand it to fully cover or push the content down. That way you avoid clutter. Like always on mobile keeping the menu items to a bare minimum is essential for a delighful experience.