It's not easy for puppy to get the idea of where you want them to go at first. Even if they do, they might not make it in time. He just can't hold it for very long – not yet. They can’t really control their tiny bladder until they are about 12 weeks old.
When we first got our puppy, she was peeping in her carrier in the middle of the night where she sleeps. Although she would cry to let me know that she's gotta go, I never could get there in time (and she was in our master bath
). I fenced off an area for her in the bathroom to solve the problem. It turn out to be a great idea and she never peep in her carrier again.
At age of 7 weeks, he will have to go potty in the middle of the night for sure (maybe even a few times). I found it much earlier just let them pick a spot anywhere in their area at first when they are still too young to gain control over their tiny bladder. I fence off a small area in our bathroom (it's a good size bath - way too big for a puppy). I put her hard carrier along with a few toys and her water in there and then lined the rest of the area with newspaper. Our baby used to sleep in her carrier when she was little and we put blanket in it to make it more comfortable. When she needs to go, she would pick a spot in the fenced off area. Pretty soon you would see a pattern as where he prefers to go. You can then slowly reduce the area that's covered by newspaper from where he has never "went" on. Take your time!! If you move too fast, he would go on the naked floor. That should take care of the potty problem at night - if you can't take him ouside in the middle of the night.
I am sorry I can’t help you on the potty-outside part since we have our baby litterbox trained. But I am sure someone else here would help you with that.