In surface properties/actor properties tag special lit. Add a light actor and set it to special lit aswell (think its under "lighting" tab in the lightactor properties). That light will now only effect actors and surfaces with surfaces/actors that has special lit tagged.
I use the default static mesh skyboxes (noob, I know ) and in order to create certain effects I will often place (for example) a reddish light near the sun to simulate a sunset. It's much more in-depth than that, but you get the idea. I guess this is the lazy man's way to doing a different looking slybox .*Kind soul to the rescue*
I never light my skybox with lights, unless I want to achieve a certain color effect or something similar. I normally just set it to unlit or crank up its AmbientGlow. Also ambient lighting isnt necessarily bad, you just need to control yourself. Don't crank it up insanely high. A value < 10 can do wonders if you use it good.
if by "comepleatly new texture" you mean open it up in photoshop, selecting the alphachannel and redoing the gradient then yes. you have to make a new texture
It aint hard. Lemme know if you dunno how to do it and ill write up how to. It's a really quick fix, easy to import and so easy to tweak too.
Neato looking shed btw.