Most walkers who become runners find that slow running provides better stress relief and a bigger mental boost than walking. Progress at a rate that feels comfortable. Gradually increase the length of your running segments while keeping them slow and manageable. At no time should you be so winded that you cannot carry on a conversation. Go with whatever works.
Many runners run every day of the week.
Others run just twice a week. Some where in the middle might be a good spot to aim for at first. Figure on running twice during the workweek with a longer run on the weekend. But again, whatever schedule works for you is fine. Keep the walking breaks.