Dede ~ Yes the offer always stands. I can't claim to know everything but I love to share what I can and help out. Again, welcome to byc.
Others might have different answers but here's mine:
Since the area I have available is shaded nicely throughout the day, will that affect the chickens?
The chickens love the shade and being as you live in one of the hottest places in the country, the shade is greatly desired.
The area is also close to my next door neighbor, will the chickens make too much noise? (no roosters here)
Chickens do make noise even the hens but the hens are usually pretty quiet and only make the louder noises when they have laid an egg and are being proud or when a predator is bothering them. I have tons of chickens and you would never know if I didn't tell you and my neighbors are very close.
Can the chicken poo be composted? Could /Should it be used as fertilizer for my vegetable patch?
Yes you can compost the poo but don't try to use it without composting it because it is too "hot" and will burn your plants if not kill them. Composted it is awesome.
What should I do if one of the chickens get sick and die? Is there a proper way to dispose of them?
If you ever have a "sick" chicken you will want to separate that chicken from the others immediately and try to treat the bird. If it dies you can bury the animal or dispose of it as you would your pet dog or cat. A lot of people will bury their pets under special trees or bushes in memory.
If you think of anything else feel free to ask. The only dumb question is the one not asked and I am sure that you will make a fine parent to your little feathered friends.