Neither, since it is "qualitative data", not "quantitative". Only quantitative data can be discrete or continuous.
(Unless your assigning a numerical "value" to each nationality type, in which case it would be quantitative discrete).
Answer 2:
If considering the percentage, eg 100% Irish, 50% Irish, etc., then it is theoretically a continuous variable, assuming an infinite number of generations. However, in terms of currently existing and past living people, for any nationality, it is a discrete variable.
It is a continuous variable.
It is discrete even though time itself is continuous.
Discrete random variable
Generally continuous but it is discrete if you look at one cupful, two cupfuls, etc (or spoonful or bucketful).
continuos
ocean depth is a continuous or discrete variable?
It is a continuous variable.
discrete
It is a continuous variable.
Date is a discrete variable whereas date/time would be continuous.
It is a continuous variable.
continuous discrete
No, Patient's gender is not a continuous variable. It is discrete variable.
It is discrete even though time itself is continuous.
No, it is a continuous variable.
No, it is a continuous variable.
Not continuous => Discrete variable. Continuous => Continuous variable.