I wouldn't worry that much either, maybe he prefers being brown? Changing colors can be a sign of stress, but it doesn't seem to always be one. Mine turns brown when he gets damp or chilled.

Frogs have very slow metabolisms, not pooping more than once a week seems pretty normal. Also, sitting very very still during the day...you wouldn't believe the number of times I've mistaken my frog for dead. I understand, it's a bad feeling. But you've got to remember they're cold-blooded and they evolved to sit very, very still so predators can't find them and so they can sneak up on their prey. Sometimes they just sit on the ground for a while.

Also, congratulations! You seem to have a friendly frog who loves to climb on you! It's not terrified and that's a good sign.

Edit: I'd raise the humidity and check and see if the carpet has any loops a froggy foot could get caught in. Other than that everything seems fine.