
I would treat him as though he was still a small pup learning to be housetrained. They don't always associate what they have learnt at home to be the required behaviour in a different environment. Make sure you take him out after meals, play, drinking, sleeping etc to encourage the idea that house training applies to all indoor places.
I remember taking my puppy to my parents' house - brilliant at his housetraining so I had no worries about taking him on to their new carpet - and he promptly piddled on their carpet :-)
ETA - just noticed the walking question. The rule of thumb is to walk them for 5 minutes for every month of their age so at 3 months it would be 15 minutes walking, 4 months would be 20 minutes etc. Once they have fully matured they can walk as far and for as long as they can take :-)