There is no “edit style” feature, so I’m not sure what such a button would do. 
That shouldn’t be necessary. If you want to edit a style, just apply it to some random text somewhere, make your modifications using the normal formatting tools for doing so, and then redefine it. This brings up the panel, where you can examine any other settings you may have been foggy on, and change them. You don’t need to actually have “body” text after a heading to change that setting to “body”.
If you aren’t finding that, either right-click on the style in the Styles panel ( Ctrl+\ or ⌃S to toggle that), or use the Format ▸ Style ▸ Redefine Style from Selection ▸ submenu for quick one-offs.
I’d highly encourage you to read §15.6.1, Think Different, in the user manual PDF, pg. 403. The style system in Scrivener is not like how you would use a word processor. Chiefly, the idea is to use styles for exceptional ranges of text, and not bother with them otherwise. We very intentionally do not have a “Body” or “Normal” style in the stock set for this reason, and make you go out of your way to set things up that way, precisely because it works against the core design of the software.
Another thing worth mentioning is that the whole heading, text, heading, text approach to writing is also a bit outmoded by the design, though to a lesser degree. The idea is generally to have your document structure described by the binder structure—compiling can turn all or some of that structure into headings as you wish, and it is at that point that the output can be fully styled, too.
You don’t have to use Scrivener in its optimum designed form, to be clear. But since it isn’t designed to work like Word does you shouldn’t expect it to provide a familiar environment—and you should expect things to be more confusing and generate friction, because you’re trying to force it to do something it isn’t meant to do. If it’s worth it to you to do that, then so be it and carry on, it can certainly be coerced to work more like a word processor.