It depends on what is your use case. Gender is categorical. Date of Birth/Annual Income/Tax Paid are in general continuous variable. But you may change them in categorical depending on your use case.

What type of variable is birth year?

An interval-scale variable is measured on a scale of equally spaced units, but without a true zero point, such as date of birth.

Can Year be a categorical variable?

With the data set above I know the months are categorical but would be year # be considered numerical or categorical? Definately categorical unless you are planning on doing a time series. Most likely categorical.

Is birth year quantitative or qualitative? So year is a discretized measure of a continuous interval variable, so quantitative. Year can also be an ordinal variable.