Need help with nano tank

Hey guys! So I have been looking into making a nano reef tank for 2 years now. I recently acquired a jbj nano cube 12 dx. I was planning on setting up a FOWLR tank then convert it to a reef tank. My question is that this jbj tank gets quiet hot because of the tank lights, so I'm planning on removing the hood and placing an led light that can support corals in the future. I don't plan on getting a chiller because I'm trying to build this tank on my budget. I have 2 questions, the first is do I need a protein skimmer for such a small tank? I can afford it but I just wanted to know if it was worth getting for a small tank. The second question is a lighting question. Would this light be good for my tank in terms of growing corals? I plan on getting torch corals, bubble corals, hammer corals, frogspawn, zoas, and elegance corals. I plan on getting the wave point blade ho led aquarium light super blue 10k

I'm planning on getting the 9in one. Thanks for the help and stopping by:wavey: