I think, by interpreting the official guidance on staying at home, the answers are:
- Once per person (under the "one form of exercise per day")
- Yes, presumably children accompanied by adults under the first bullet of "stop public gatherings"- as long as family/same household
- It's not about the dog, so one person can walk two dogs once a day
- Not specified, so whatever constitutes a "normal" walk
Others may have a view.
In practical terms, my dog goes out for three short walks a day, different person walking him each time where possible. I have a garden, so he doesn't need to be taken out for toilet breaks and I could reduce the number of walks if necessary. I'm keeping him on the lead at all times, to avoid the risk of him running over to other dogs (despite pretty good recall) and making social distancing from other dog walkers more difficult.