part two
frequency of bowel movement has more to do with how much waste there is to eliminate. Some dog foods advertise that they are more completely digested so less for the owner to pick up but i would be a bit wary of these for two reasons. The first is that they might be less filling for the dog and lead to scavenging habits, the second is that IMO some indigestible fibre content is necessary for good health and to prevent constipation. My boy who has food allergies is now on a special food. it leaves very little residue so we have had to added boiled carrot to his diet to make him feel full and to make his motions bulkier and softer (are you all enjoying your breakfasts reading this?)
If by regular, you mean predictable, that's pretty easy, on waking, after feeding, after exercise and before settling for the night. As i said, i reckon that the problem that you have is that he thinks its the right place to go. Taking a dog outside to teach where to do business is not like taking them out for play and exercise. you go out with the dog and don't let it have fun, don't walk along play with the dog or talk to it except to say "hurry up"or whatever phrase you choose to associate with toiletting. If you housetrain a dog in winter lol this happens normally because you are both cold and wet and tired if its at night.
with respect, I don't think neutering or changing food will help here, you need to go back to basics, clean off the scent of the mistakes and calmly and patiently teach your dog where the right place is. He WILL twig eventually.
We got our two at 7 weeks old from a lady who said they were paper trained...they had never been out of her house. What she meant by paper trained is that she had kept them on newspaper and cleared up the messes!!!!! nightmare! AND with two at once...calm patient perseverance and thorough cleaning up of accidents WILL work.