Not sure if the mass unstacking thing is possible so cant say for sure if there is a mod. As for the auctioning part there are a few mods that have mass auction posting for large amounts of items. Even just having the alt-click of auctioneer would assist. Though that is a rather hefty bit of addon just for that function.
Mass Auction is one that comes to mind but its been a while since its updated, may still work though.
This
Quick Split may ease the splitting process some. Same as above, its been some time since an update was released.