The auto-relist allows your auction to auto restart if a bid/sale does not occur. If your auction is for 6 days, then after those 6, it will re-list for another 6. Up to the 3 times you setup on them. Re-listed auctions do not return to the front page. They are only on the front page the 1st day of the 1st auction. The front page rotates daily with newly listed works only. However, your re-listed auctions will appear on the "ending soon" and "recently listed" quick searches that DPW has built in. I know I have had no bids for the 1st or 2nd re-list, but then suddenly on the 3rd a bid pops in.
You can easily do your auctions with no re-list time on it, then switch it to buy-it-now when that ends without a buyer. I think it's really up to the individual artist. I list to run my auctions with a 2 or 3 re-list option before going to Buy it Now.
And yes, it is only 1 new painting per day on the front page. I often setup my auctions to start over a series of days (say 7), each one starting on a different day. Each one re-listing once or twice.
What DPW will allow you to do, is in your art tracking screen, you can bump up a painting that is 6 months old (or more) so that it appears on the front page again. DPW would prefer a new painting on the front page, but quite honestly, after 6 months I wind up with a whole new set of eyes seeing it. And I often sell these that way. I may paint every day, but I can't always finish a painting in 1 day, so I will resist my older ones periodically so I keep my name out there. A painting can appear on the front page only 3 times, each being at least 6 months apart (which basically gives you 3 chances to sell your work within a year and a half). This is true whether it's an auction or buy-it-now (or even email to ask the price).
Hope this is all helpful (and all makes sense). You will find your own rhythm as to what works for you with posting & dates. Good luck!