Yes, walking builds leg muscles......to an extent. The problem is at some point you stop progressively overloading your leg muscles.....ie you walk for a certain amount of time or a certain distance, so as soon as you can do that distance you are no longer sending your body the message "I'm being forced to do something hard, so I better add more muscle"

I love walking, and walk 50 minutes 3-4 times a week, but it is not a substitute for weight training. Walking 50 minutes and leg pressing 500 lbs are apples & oranges.

Yes, muscles grow during rest, not the workout. So for the first few months, until the time/distance gets easy, walking every other day would be beneficial.

I suggest beginners weight train each bodypart twice a week (working the whole body at one time) and only after a year of training split out body parts for more isolation.