Yes you can just melt the butter use same amount. it should work well.
Well, you probably COULD substitue butter for oil, there are several things you have to consider. First of all, butter is not 100% fat. Its acctually only about 81% fat. The rest is water (about 15%), milk solids (2%), and salt (2% unless its unsalted butter). Also, because butter is solid it doesn't interact with the other ingredients quite like oil does.
In sort, while you could do it, and the cake would be edible and rise and look ok, it might not tast quite as good or the texture might be off or something. Not a big deal, but if its a really important cake, I wouldn't risk it. Hope this helps!
P.S. There are some recipes where the difference might not be noticed at all, and the smaller the amount the less diferences there will be... Just know that they are not the same thing.
It's a box of cakemix. Experiment to your hearts content. If it doesn't rise properly, you can always bake another one. Enjoy! 
In my chart of substitutions in my cookbook, it says to use a 80/20 ratio. In other words, when the recipe calls for butter and you have oil use 80% of the total amount. If you have a recipe that calls for oil and all you have is butter, add 20% to the total. For example, I have recipe that asks for 1 cup of butter ....then I would use 3/4 cup oil plus just a little (because 3/4 c would only be 75%). Does any of this make sense? I'm not very good at explaining things on the computer.
I found this chart doing research for another post this should help you.
http://www.goodcooking.com/conversions/butt_oil.htm
According to cake mix directions, you melt the butter and use the same amount as if you used oil.
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