The date can be considered both categorical or numerical variables depending on the context of the problem. Categorical: Suppose the data is only a particular day of the week and is captured in that way. Then the data can be easily converted to a category (day) of the week. Again, the context is important. Obviously date is ordinal, as there is an order if the date is recorded with an order.
Generally, date is an interval variable as there is no absolute zero and the difference makes sense. I.e difference between 13 October and 12 October would be the same as the difference between 10 October and 9 October. When referring to Time and Date as variables, the context is extremely important.
Day of the week is a categorical variable.