C&R for trout during the normal Zone trout season, artificials only - no bait. Look at the map in the regs to see what areas of both creeks are open starting in April.
99% sure you need a license to fish a body of water that flows through your own private property. Maybe someone who knows for sure could confirm this, or correct me if I'm wrong.
I've never fished either, but I've spent time on the upper Abiqua, great looking cuttie stream. I've fished the Pudding right below where Abiqua dumps in and pulled some nice cutties. Just used 1/16th oz spinners, various types and patterns. Could definitely go with a little bigger lure. The fish fight good and are fat. I'd have to assume that below the deadlines on both creeks (where fish can travel as they please, not confined by falls) you would find fish of similar size to what I caught in the Pudding.