Probably not that much longer than a developer sandbox as the distinction is really the maximum capacity, not what is copied. But you will need to run scripts to populate the data that you need.
Config sandboxes go into a "fast queue" and are processed separately than the "slow queue", which is for organizations with large amounts of data (and usually takes longer). In general, a config-only sandbox may take as short as an hour, but it could take over a week if there was a long queue (usually during preview refresh windows/new releases).
Usually not long, however sometimes it can take a few hours and Salesforce do not have any SLA at the moment regarding maximun refresh duration.
I would encourage promoting these ideas:
https://success.salesforce.com/ideaView?id=08730000000KYPSAA4
https://success.salesforce.com/ideaview?id=08730000000BrGAAA0