The panting is normal unless you see it being strained or something. My boy pants most the time to some extent, in fact my 2 year old thinks that is what he "says" vs the pug who barks. haha (she imitates them both) As for the peeing, he should be going as often as any other dog. Is he drinking a lot of water tho? My boy was 9 months when we brought him home and he didnt eat hardly anything for a few days. I am not sure if he stopped drinking water too, it was a long time ago now. Maybe your boy is still trying to adjust and hasnt gotten to want to eat and drink so much yet? I would watch to make sure he is drinking enough tho, maybe even try to get him wanting more with little ice cubes? If he hasnt been pooping it is probably because he isnt eating as much also? He should come around and eat but the water is very important. Maybe give some healthy veggie snacks like carrots, green beans, lima beans etc... There is at least water in those as well so that will help. What kind of food is he on, just curious. Getting him on a good food is important for sure if he isnt already.
Oh and welcome to the board. Ask any and all questions you have, we have a good mixture of people on here who can answer most all of your questions. Please share more pics, we love them here. Your avatar is cute!