Newbie Coop Location Questions

I'm planning my first coop, for approximately 3 birds. I'd like to put it on the West side of my house (which is in Las Vegas.) The area I have to work with is nearly 550 square feet. (See picture below for more details.)

Initially, I was hoping to put it in location "A", and give the birds all the area from "A" to the front gate (about 550 square feet). My concerns with this location are (1) it's only about 10-12 feet from my hot tub, (2) our typical wind pattern has my hot tub downwind of this area, and (3) it's awfully close to our community mail box (across a 6 foot concrete wall, and I'm trying to keep chickens a little "discreetly" in my HOA, although my neighbors are pretty cool and most wouldn't mind even if they knew they were there.)

So, my next area of consideration is location "B", which would give the birds around 380 square feet. (I want the coop at the end of the run, not in the middle.) It's 24 feet from the hot tub and further from the mailbox. Other possible locations are "C", "D", and "E".

Finally, I'm planning to cover the gaps on the sides of the front gate, so the run would have only one fence. The run would be from the side of my house, to the far wall (with the black gate), to the side concrete wall, to a to-be-constructed fence on the nearside. I don't think that I need to fence in the bottom (ground) of the run, because our ground here is incredible hard, and no gophers or other animals can burrow up into the run. I'm hoping to not have to fence in the top (roof) of the coop either. I'd plan to close the coop door on the hens every night, so they'd be secure overnight. I don't see many wild animals where I live (other than a coyote a mile away, and he'll probably be moving on due to some new construction). I could be wrong, but I don't see hawks flying around in the sky.

Questions:

1. Is location "A" too close to the hot tub? (As this is my first coop, I don't have a feel, yet, for how many odors I'll be contending with if the coop is 10-12 feet away from the hot tub.)
2. Is there a breed I should consider that is known to be less vocal and will not always be tipping off the neighbors to their presence when the neighbors are getting their mail?
3. Can I try leaving the top (roof) of the run unscreened, initially, and see what happens? Or is this just always a bad idea?
4. The wall at the far end is only 5½ feet tall. Is that high enough to prevent escaping birds?

Thank you for your help.

Depending on what your concern is, each location has pro's and con's. If the coop is close to the hot tub, you may smell the coop from time to time, especially during wet periods. If you clean the coop regularly, it won't be an issue. From a noise perspective, chickens are not normally loud (assuming you won't have a rooster - they crow all the time, morning, noon, evening, night). Mine are noisiest when they are laying an egg. They announce it to the world!

If your HOA won't approve of the chickens, I would work on getting them to change their policy. Once you have chickens, you may not want to get rid of them, and HOA's can get very ugly in their enforcement of their rules.