On my system, when I press F6 the contents of the address bar in Firefox are selected, just as you wish. The same behaviour with Iron (a derivate of Google Chrome).
To select the text (if any) on the search bar on Firefox, then you can press F6 and then Tab.
About the "black text area" I don't know; maybe you mean "blank text area", meaning that once you start typing, the (selected) text is substituted?
In Opera, you press F2 to open a window where you can type a new URI.
For searches, I have configured several search keywords in Opera's integrated search, so I simply press F2 and type, for example,
d recipe, to search for the word "recipe" on DuckDuckGo.com or
doi 10.1126/science.1100199 to go to this paper.