Help convincing parents, and a bit of information needed. (I think it goes here...)

First off, I'm not exactly sure where this would go. I need permission to raise baby chicks in the first place. (Well, maybe there's a way to do it in secret, but that's really irresponsible and a terrible idea.)
Secondly, me and my sister are planning on getting at least two companion silkies, three at the very most. My sister is in charge of paying for it, and I'm the one researching, and persuading the parents.
We plan on keeping them indoors. Therefore, I need to know the minimum space a bantam needs if it is allowed to roam the house, (supervised, of course) for at least an hour or two each day. That includes time outside, since I've read chickens like to eat plants and bugs. We have three cages, an old rabbit cage with three square feet and two floors, a parrot cage with about three and a half square feet, and a pigeon cage with similar proportions.
I also need to know if silkies are loud crowers, and if crow collars really are humane and if they work well. My sister is willing to buy a brooding lamp, chick starter feed, a waterer, diapers, and collars, is there any extra stuff we need? Are newspapers an adequate substrate?
I live in a relatively large two-floor house with a small yard. How hot will the brooding lamp need to be in a house about 60-70 degrees Fahrenheit, and about what age would I be able to stop using it? That's about all I need to know that I couldn't find from other sources.
I know my Dad wouldn't really need any persuasion for this project, he bought an amazon once and it interrupted my mom's singing so it went to my uncle, she's the one who needs it. I know just asking for chickens won't get me anywhere. I plan on writing a letter, full of information on silkies and how to care for them, some problems and how to fix them, (like pasty-butt) some pictures, and ways that it's beneficial. So far I've come up with a few things, like it being educational, but I won't say anything about eggs because silkies don't lay much. In the letter I don't plan on mentioning that they're chickens right away because that will discourage her and trigger immediate disaproval.
I also thought it may be important to note that I have two younger brothers, and let's just say they aren't too bright.

Good luck to you on your parent-convincing mission!

First off, you might have an easier time persuading your mother if you keep the chickens in a coop, outside. You can use diapers and all that to take care of the poop part, but those diapers will do absolutely nothing for the dust and dander the birds will create (and they'll make that mess no matter how clean you keep their cage). That being said, I really believe a chickens place is outside scratching in the dirt and eating bugs, though I can understand why people would keep them as house pets. An hour or two outside of their cage isn't going to cut it, chickens aren't like parrots or other cage birds, they need space.
You should also consider getting 3 instead of 2. If something were to happen to 1, and you just had 2, you'd be left with a lonely chicken, have to search for a replacement and then go through the process of introducing new birds to each other. My Silkies crow loud enough, they aren't as loud as some roosters I've heard, but you'll know they're there. And, that crow is going to sound a lot louder if its inside your house. I believe the rule of thumb as far as space goes is 2sq feet per bantam? I can't really remember, but bigger is always better as far as space goes. You wont notice issues when you have more space than you need, but lack of space is a nightmare.
As for your brooder, you'll want the temperature under the lamp to be somewhere around 85-95F the first week (decrease temp by 5 degrees each week), the rest of the brooder should be room temp, so they don't get over heated. Newspaper will work as bedding if you shred it. Its pretty slick when left in sheets and can cause slipped tendons and splayed legs, paper towels are an excellent bedding choice.
My biggest piece of advice, be as up front and honest with your mother as you can. Tell her they're chickens. Explain that they're educational, they'll lay eggs your family can enjoy (my Silkies are actually pretty good layers, until they decide they want to hatch chicks), they'll help keep bug populations down since they like eating them, you will no longer have to throw away left over food...the birds can enjoy them, their soiled bedding can be used to fertilize garden beds and house plants (if that's something your family does). Explain all of the ins and outs of chicken keeping, why you want to keep them and be up front about any draw backs like crowing, ect. The last thing you want is to get the chicks having left out details only to find out that your mother doesn't enjoy them because of that and makes you get rid if them after you've become attached.
Silkies are an extremely friendly, docile breed (and they're adorable!). They're a great choice for beginner poultry keepers, but they do come with some drawbacks. Brooding (which is a trait I enjoy, but many others don't) for example, is something the breed is most known for. How will you handle that when it happens, break them, give them eggs to hatch?

Anyway, I think your mom might be a little more receptive to the idea if you figure out a way to keep them outside, considering her aversion to the amazon's noise. And believe me, as a parent, honesty goes a long, long way. Leaving out little details isn't exactly lying, but its not telling the whole truth either.

Do you intend to do 4-H or show your chickens? That might also help convince your parents, if you join a club or pick up an extra class at school because of them. Educational extracurricular activities always win points with the parental units.

Best of luck persuading them.

I agree with the above post. You might also consider a trial run. I bet you can find another chicken person in your area and see if you can borrow a pair for a week or two to demonstrate to your parents that you are responsible and that it will work. Heck in some areas you can even rent a chicken. Comes with everything you need including the chickens. Another thing you might consider is going with adults instead of chicks. So much less that you need immediately, like brooders, heat lamps, etc. You will pay more for the pullets up front but you will know that you have pullets and won't have to worry about the crowing to begin with. 4H or other rural organizations can help you get started.

One more thing. Even though they are not big layers, we LOVE to eat our silkie eggs as they are very rich. Not enough for breakfast very often but add a definite richness to you cakes and cookies.

Have you researched Silkies' special needs? They aren't like standard chickens, and not just in size. Their feathering, even when reaching adulthood, lacks the ability to insulate against low as well as high temperatures, so they really do well indoors where the temperature is constantly moderate. Arizona, unless you're at high altitude, can get very hot in summer, and Silkies would have a hard time outdoors. They also don't do well when the temp gets down below 50.

I have doubts your bird cages are going to be large enough. While Silkies don't need as much square footage as standard chickens, they like to hang out together, and if you have them in separate cages, they will be unhappy. Unless you can figure a way to combine the cages so they can sleep together in a pile, because they prefer that to roosting.

As for substrate during the brooding period, most of us like pine shavings, except for the first few days while chicks get used to what "food" is and is not. Some use paper towels. Newspapers aren't absorbent enough, and can be slippery for teensy feet. I'm thinking of using puppy potty pads this spring when my chicks arrive. They will stay in place much better than paper towels, and the chicks won't eat them. Yes, chicks think everything is food, just like human infants.

I admire your decision to research this project thoroughly before approaching your parents. This will serve you well out in the world of commerce where you will need to deal with supervisors and bosses. Just as with your parents now, bosses are impressed with new ideas and problem solving, but only if you can give it to them all wrapped up in a pretty package with a bow on it, all the "work" already done so you aren't giving them any new problems they need to deal with.

Since you said you live in a "large house with a small yard" I take it you live inside the city limits. If you do, then you need to find out if the city allow chickens inside the city limits. Most city have regulations on what animals they allow and chickens, I believe, are considered livestock...though, I could be wrong about that. But, you need check with the city before purchasing any chicken...and it doesn't matter how big of a town you live in, always check with city hall to see what the town regulations are.