Is there a way to use Testlink for the management of these type of tests, and behavior-driven development?[/QUOTE]
TestLink isn't a good tool for exploratory testing.
TestLink is generally operates on the concept of test cases and coverage percentages, where as exploratory testing generally goes on Charters and timeboxes.
What you can do (but I wouldn't recommend it) is create a separate project with custom fields for things like areas to test, a genera text area describing the test results, and a notes text area to describe areas to explore next.
A list of different areas there are in the app for example something like.. which is prepopulated in a text area. Then as a user is reporting test results, he or she can quickly
[ ] authentication
[ ] settings
[ ] user management
[ ] profile management
[ ] live feed
[X] photo album
[ ] privacy settings
Then for different exploratory tests, you can describe them in terms of doing a 'tour' (coined by James Whitaker)
I think however, you might want to use a CMS to manage that.