Well, lighting wouldn't HURT .. but you don't need anything but your typical tube lights. The things that get expensive in saltwater tanks are the high end fixtures that help corals grow. Fish for the most part require considerably less lighting (think freshwater).
In your case, yes you could use some of the tank water to help kickstart your biological load in the QT tank but with that could bring water born ich parasites.
If it were me I'd put together a 10g with a powerhead OR small HOB filter for water circulation/aeration. The HOB filter might be ideal here since that will help with detritus. (poop/etc) but will add more expense. IF you wanted to provide any lighting a small wattage clip on reading lamp would be more than enough, but as I said my QT tank is NOT lit (the bulbs are burned out) and the fish are fine (the tank is near a window with the shade mostly closed).
As for treatment either Cupramine or Hyposalinity. Hypo would be the way I'd go but with a 10 gallon tank you are going to need to watch evaporation closely, because you need to keep your salinity at 1.009 and small fluctuations can bring it up to 1.010 and above pretty easily. Cupramine doesn't have that drawback but you'll need to be able to test for it to keep it at the recommended dosage for the recommended period of time. If you chose the Cupramine route and you use a HOB filter for filtration and circulation you'll need to be able to remove the carbon from it otherwise it'll take the cupramine right out of the water.
These are just my two cents on the issue after facing Brooklynella with my clownfish. I have 3 more weeks to fallow my display tank before I can move them back.
Also since the tank is not truly cycled watch closely for ammonia spikes. Water changes will help here. If you can find them (I haven't found them locally) you can get ammonia alert badges. Stick one inside the tank and it'll change color as ammonia rises. They're good for 6 months I believe.
Once you've used your QT for the recommended treatment time and fallowed your display tank for ich, giving the empty/fishless QT tank a little bit of fish food regularly will help keep the tank 'cycled' by giving the bacteria stuff to consume.