Structured walks/exercise can be very tiring very quickly for pups that young. The recommended forced exercise length that I have seen is no more than 5 minutes per month of age, but don't force them if they seem tired or don't go as long as that, go at their pace. Forced being anything on leash, constant pace, constant speed, hard surface, etc. Free play is free game! The puppy can go at their own speed and slow down when they desire, which is much better on their joints.
Also, please be careful where you take them for walks! Without full vaccinations, they are vulnerable to all the nasty stuff out there on the ground, from other dogs, etc.
It's good he knows the back yard is where he should go! He has a very tiny bladder, so if you don't catch him or pre-emptively bring him outside often to let him go, he will go in the house. If you keep it up, he will learn that outside = yes and inside isn't where he should go. Just stay consistent and reward him for going outside every time. If you want to train him to use a different area, take him to where you want him to start pottying. You can even begin to work on teaching him a potty command (which just takes time and gets much easier as they are older and get to know where/what they're doing with potty training!)
I believe the recommended assumption is that a puppy can "hold it" for about 1 hour per every month of age. So at about 12 weeks, up to around 3 hours or so. However, I wouldn't expect that standard. Play, activity, more water consumption all lead to a puppy that will potty more frequently and without holding it. I assumed my pup would only hold it while crated, and gave frequent potty breaks outside for a chance to go before any play/activity and before resting.
The behavior is all normal if you ask me. And it will get better as he gets older with proper training and attention.
I hope these help, and I learned this from my own questions and research on this forum. There's a wonderful search function that you can find tons of other experience as well from others! If I didn't properly answer anything, hopefully someone else will chime in.
