First bay yes, your skimmer. You measure the bay size, and choose an appropriate skimmer for it.
This isn't mandatory, but a lot of people do it this way.
Second chamber, would be a nice fuge section. I recommend LR and plants, leave sand out of it unless you want to get complicated and start doing things like LS/Mud/DSB ect.
A simple easy to do method is using golf ball to fist sized pieces of live rock, or base rock that will eventually become live inside this section. Toss in a few crabs and snails, and it will work pretty nice.
You can also do just plants, and cheap light over it.
Or a mix of both macro algae/LR.
By keeping this bare bottom you will have detritus buildup over time. It will be a gray layer at the bottom. Since its bare, it will be easy to vacuum up every few months when doing your WC. If you have LS, your buildup will be significantly less, but you wont be able to suck out the excess. Then you have to turn to sand sifters to do the work.
AS you can see, you have lots of options, nothing is absolute. You can get really creative and do just about anything you want. Lots of possibilities. I just named off a couple quick ones, that Ive personally used and like.
The third chamber is the return pump area, this is where you will do your water topoffs(make sure your only doing freshwater, since salt stays in the system).
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Moving on to the next set of questions:
Water coming from the tank is gravity fed. Basically your return pump pushes water up top, then it overflows, and falls back down. Best method is the overflow box. Go to glassholes dat com and check them out. They sell overflow kits and have easy to follow instructions. It involves drilling your hole in the side of your tank, and placing a bulkhead and overflow box over it. Drilling glass is actually really easy if you do your research first, and watch videos. Its cake.
Good luck. Welcome to SW. Go reef or go home^_^