I would say the peeing is normal. Not sure about the lack of poo... 2 days seems long for a puppy to go without though. Is there a vet you can visit?
As for going to the bathroom in the house, he is still just a puppy and doesn't know any better. For potty training, your best bets are:
1) PREVENTION. Don't give him an opportunity to have an accident. Always keep a watchful eye on where he is. You can keep him on a leash if you find this difficult to do, and just attach the leash to your belt loop while around the house so as to keep him nearby.
2) If you cannot supervise him for whatever reason, I highly recommend crate training. Most puppies won't want to eliminate in such a small space, which will enable you to do errands or whatnot without worrying about what your puppy is chewing, peeing on, etc.
3) Learn your puppies schedule. For example, when my dog was a puppy, he consistently needed to be let out when he woke up, when he came out of his crate, and about 10 minutes after he had eaten/drank. Because your puppy is a little older, this schedule may not be perfect for your dog. However, it is really important to get him out frequently so as to encourage the association of outside and bathroom. When your dog does go in the right place,
reward him! Tell him what a good boy he is and offer him a treat or play. If you take your pup out and find that he doesn't want to go, one of the best ways to encourage the bowels to get moving is activity
Whenever my dog has a good run around, he almost ALWAYS goes to the bathroom after.
A few things to keep in mind:
If your puppy has an accident, you have two options.
A) If you catch him in the act - Walk over, pick him up (even if in mid pee!) and say 'woops' or 'oops' in a neutral tone (neither angrily nor happily). Take him immediately outside and give him the opportunity to finish outside. If he continues going outside, praise.
B) If you find the mess after the fact - Do not get angry with your puppy. He will not be able to understand why you are getting angry unless you catch him within about 2 seconds of finishing because he simply will not put two and two together. At this point, you simply have to clean up the mess and remind yourself to do a better job of supervising him. Make sure you use a cleaning product that will completely get rid of any traces of the smell of urine. If he smells pee, he is more likely to go in that spot.
Good luck