I think it counts! I sometimes take a walk when I'm at home. I looked at my BP Doctor and it also showed calories burned.
Of course! As long as you move your body, it's exercise
Do you mean walking around the house in the course of your day? Usually people need a little more than that, although every bit helps.
Any type of movement (even house/yard work, etc) are considered exercise and better than not moving at all. It's no fun to be outside, walking on a rainy day, so you could try to come up with a different type of exercise for those days. For instance, I have several different weights I can use, plus there are exercises for which you can use just your own body weight. You can search YouTube for these exercises. You can try searching for "Body Weight Exercises" or something on that order.