Hi,
1. It could be several things. The filter normally takes automatically the values of the custom field. If you have activated the "dynamic display" setting of the filter, it will only use the values that have been selected in the custom field in the products of the listing currently displayed. So if you haven't selected any value in the custom field of the products of the current listing, it could explain the problem. Another possibility is that your custom field doesn't have any values configured in it. For example, if you've selected the type "text" or "text area". In that case, the system is not able to use the values you entered in the products to fill in the filter. You can however use such custom field in a "text" filter in order to have a search input box as filter.
2. With the price filter type set to "cursor" and with its "dynamic display" setting activated, the filter should automatically use the min/max prices of the products in the current listing as range for the filter. So that's possible yes.