What is a reasonable billing approach to art / setup time incurred while sending a project to production?
That one relates to the demographics of your target group and how you want to handle things. Want it built in or separate item.
In my mind they are. If you don't place value on your skill, time, labor then how can you expect your customer to?
In the embroidery/quilting industry where I do design work, there are lots of ways that a cheap/free design can kill you production wise. That's a little bit different then what you would deal with in the print world though. So even a higher priced design can save you money in the long run over the course of that production run (something that some embroidery shops don't get, especially the stay at home "shops").
Should the art time consumed in house by a hourly employee be billed at all?
Yep, otherwise you can end up in a situation of income not greater then expenses. How you bill it is something else.
Is it better to accurately bill the art by the minute or round it out to the hour?
Hourly, or you could figure out some flat rate that on average you'll do better at more times then not.
Mine, again, is a little bit different. It's by stitch count which means I could work on a design for 5 hrs or 5 minutes and the pay will be the same if the stitch count is the same. Over the long haul though, a stitch count method is the best overall fair approach for me and for the end customer. Although, I do have a flat rate system for embroidery font conversion as fonts usually are done on a flat rate system and not stitch count.