1. I have no experience about money order. If you open your account, and deposit your cash into it, you can get the certificate at once. Bank will charge you about no more than 15 dollars (I can't remember).
2. In fact, when I rent my current apartment, I only have 1500 dollar in my chequing account. I don't think there's any limitation on this.
3. Yes, if you are not serious about the location, price, etc.
4. You must pay them before you could get the key of your house. One of my friends deposited only 2 months rental fee. So, I think it depends.