Like everyone else said, if you were running before getting pregnant, then it is absolutely safe! Just make sure that you aren't over-working yourself.
A general rule of thumb is if you can carry on a conversation while working out, then you are fine.
Yup! I power walk every day and I haven't slowed down (well...ok, I did for a few weeks when my morning sickness was really bad, but never stopped completely), I'm back at it. As long as your body is used to it and you aren't overworking yourself, then definitely continue the exercise, your body will thank you for it later!