Hi,
1. Well, if you don't set a price, or set a quantity of 0 for your product, your users won't be able to buy it as the add to cart button won't be displayed. Then, you can use the options "Display a contact button on the product page" of the Display tab of the configuration to display a "contact us" button instead so that they can contact you for that product.
2. Indeed. Unfortunately, the queries for the filter to load the product listing by searching for the prices in the variants would have been too heavy, so we decided to not handle that case. Thus, you will have to also put the price on the main product (you can add several prices if you want).