Is it considered to be like the fast of David, to fast one day and break the fast the next, in a fixed pattern, such that specific days (Sunday, Tuesday, Friday) are designated for breaking the fast, and the remaining days of the week are for fasting?

The fasting of David (peace be upon him) is the best of voluntary fasts. It involves fasting one day and breaking the fast the next. This is superior to perpetual fasting because it is more difficult for the soul. If someone wishes to start it by fasting on Saturday, they would break their fast on Sunday and fast on Monday, and so on. Fasting two consecutive days is permissible, but it does not align with the fasting of David.