Is birthday a categorical variable

Answer 1

No, date of birth is an ordinal variable. Ordinal variables are similar to categorical variables except that an ordering of the values is possible. With date of birth there are obviously many possible day/month/year "categories" but they are discrete and can clearly be ordered from highest to lowest or vice versa.

A categorical variable might be something like animal type. Each animal type fits into a class, but there's no intrinsic ordering of cow, sheep, pig for example.

Date of birth itself is not an interval variable either. It doesn't make a lot of sense to talk about "average date of birth" for example. But of course, date of birth can be convertedto an interval variable (i.e. age) simply by subtracting it from another date (e.g. today's date).