Great improvement! Even once is better! If you can catch him about to go and can get him outside in time he will soon learn that he is meant to go out!
You are lucky to be there all day with him. I have always been told not to free feed, or feed and leave it there so that they can eat when they please. Mine get 15 minutes eating time so depending on the meal they either gulp it down or pick it slowly! after 15 minutes bowls get picked up. once you know how long your dog generally takes between eating and depositing (ha ha!) you will soon learn when to put him out after his meal!
oh it's so hard when they whine to come in and we have to be firm

It's so hard not to spoil them every second of the day with those cute little faces!
As for newspaper, i gave up on that very early on! Taylor would chase it around the floor all day and then do her business off the paper anyway! the older she got the better she got at destroying it and I would come home to a room full of shredded paper and wee everywhere! I have a weak stomach at the best of times! lol!