Questions before switching

 I currently have a wordpress site and I'm using a customizer, however it is very limited and wanted to see if this customizer has the following features. I checked the docs and some demos and these are the questions I have remaining. 

1. In the customizer along with the color templates of the shirts can I also add an area that has different sizes for example small, medium, large. Where the user can add how many they want of each size. Then before adding to cart for the price to dynamically change?

2. In the customizer can I have the color of the shirt dictate what sizes are available? So for example if a user selects Product A t-shirt which comes in red, white, or blue. Then when they select red it shows its available in XS and Small. When they select white it shows, XS, small, L, XL.

3. In the customizer can I also have sub attributes. So to piggyback off question to. Along with sizes. Let's say they select Product A and color white. The sizes are broken up in youth, womens, and men. So they can select white. Then have the option to order a small in either womens, youth, or men.

4. I saw you can save a design. Is there a way to store it? For example if my site allows users to create an account. Can i create a page called "Saved Designs" where i can place a shortcode or something on this page that displays all of the users saved designs?