Starting my first 50gallon reef tank, need some help!

My wife and I are setting up a reef tank for her Mom as a gift using her Mom's old 50g tank from the Philippines. We are both complete beginners without any experience whatsoever. I've read a lot the past couple of weeks, which cost me a lot of sleep, but with all the products you can get, I'm kind of confused as to what I really need. Yesterday I started the cycle but I still need pumps and proper lighting before moving on to adding corals and fish in a couple weeks.


So here are my questions:

• What lighting do you guys suggest for an aquarium with a roof where heat can easily get stuck? ( I'm not allowed to post any links yet, otherwise, I'd show you the aquarium)
  
• How many pumps and what overturn rate do I really need for beginner corals ( I'm interested in toadstools, blastomussa, elegance coral)? I've read numbers from 10x to even 75x the tank size. And where should I place the pumps?
  
• What is the best way to measure nitrate and ammonia levels? I saw a thermometer-like device you can put in the tank. Are those reliable?
  
• What filtration media should I use to keep ammonia and nitrate levels low?

I also have some non-equipment related questions I haven't been able to find answers to but I'm not sure if this deserves a single thread so I'll just ask here:

• When performing water changes, do I need to use freshwater or saltwater?
  
• Is it really that harmful to use conditioned tap water?
  
• Do I need to feed corals separately from fish? If so, what do I need?
  
• Do I need to use supplements such as Iodine, Magnesium trace elements etc. to maintain the tank? And is there a difference between supplementing trace elements or certain elements individually?
  
  From what I get, trace elements are made up of all the elements you need so you don't need to supplement every element individually. Please correct me if I'm wrong.