I just started working with fondant and I have no clue what I'm doing.
Is it best to leave it on the counter if you want to harden and stay that way?
What is the best way to store it?
Particularly I'm doing a beach towel with multiple color stripes...what's the best way to adhere the stripes to one another??
when i dry/harden my fondant accents, i just set it on the counter to dry, sometimes i stick them in the freezer to speed the process along.
as to the towel stripes.... are you attaching the towel to a cake? without knowing what you are trying to do, if it were me, i would attach it with buttercream. if you give us some more info, we can try to help better.
For the towel, you could roll out one larger piece of white fondant, and then "paint" it in stripes with a gel colour.
Leaving fondant out will help it dry. I put mine (and store it) in a covered container to keep off the dust (but not necessarily air tight as the fondant may not dry) and in a cupboard to keep light away from it - colours may fade in the light.