Laptop Purse

The rules of air travel that I can have one bag and one personal item such as a laptop, handbag or camera.

Yes, the laptop would be considered as your personal item if you carried on by him or in his own case. You can try to stick your purse in your backpack and carry your laptop separately, however, if you decide to use it during your flight, you will likely be asked to stow your hand luggage in the main storage bin Unless your backpack and purse will be placed under the seat in front of you.

Yep, you can.

I agree with the rest of the responses since I used a similar method to bring more than one point to board a plane. I often pack my camera in my hand luggage and can bring an element such as a laptop on board without any problem. You may want to consider putting your bag in your hand luggage and carry your laptop if you plan to use the laptop during the flight. If there are documents that you want in your bag, it can be more easily transported in a secured (ie zip) your pants pocket or jacket or even place them in your notebook laptop.

Yes, as long as the backpack and handbag are the size allowed by your airline.