With this question I'm hoping someone with experience in this field and might be able to suggest how to treat behaviour of uncontrollable biting with a dog puppy.
Me (25 yo) and my mom just got a Border Collie, Blue Merle puppy two weeks ago at age of approximately 3 months. Previously, this dog was with another owner where this puppy was staying outside with other pups, however now we have him inside the house most of the time. He looks healthy (digestion, fur, teeth, general behaviour) and we also try to provide him with a healthy lifestyle.
The problem discussed in this thread is his excessive biting when someone is playing with him. I know he is a little puppy and his teeth are growing, and possibly he's in that phase where gum itching takes place, however I think his biting cannot be controlled. For example, initially when trying to calmly play with him, he shows his excitement and usually cannot hold back to burst forward to play. I kind of like it that he starts licking and all, but that licking soon turns into mild biting, and if I continue to calmly pet him, he starts biting more and more. Eventually also biting clothes, slippers, or if he is ignored, he starts biting literally everything he sees (even the floor sometimes). No gesture or raised voice prevents him from stopping or at least calming a little bit. Only if he is separated in some other room, he eventually cools down.
Might not be a good idea, but I tried slightly hitting his nose or butt when he is in the peak of his energetic biting. However, he understands this more or less as a game and continue to rip apart everything that he encounters. Please note that I would never go as far with hitting as hurting him in any way. The only reason of hitting him slightly would be to show him something like "Hey, this is the limit! You shouldn't pass it!".
Here, I would like to add that he has plenty of soft toys to play with (my hands sadly included as well ) and he often gets some natural dog-like snacks for biting. And currently, I'm waiting to get him vaccinated so then I can take him to long in-nature walk which I'm sure he will love. And maybe he will have a bit less energy for biting during the day.
Also, he pooping and peeing a lot (like +15 times per day of peeing would be a reasonable value) This feels more reasonable. However, I hope he will learn to control this over time and also somehow let us know that he needs to pee/poop, so then we could let him outside to do his stuff. Now, pee puddles are everywhere and we have to watch our step as if we would try and cross a minefield!
I'm hoping to find any good book on this type of breed that would explain how to raise them and possibly how to teach them some fundamental as well as more advanced stuff. I'm sure this all is possible, since they are said to be very intelligent breed.
Here are few pictures of him: