Ordinal Variables are when there is a natural ordering to the data [ hence ordinal]. E.g. Income as Low, Mid, High is a ordinal variable.

If your variables have such orderings then they will be Ordinal variables.

I guess, Gender won't have such order. It is just a factor or categorical variable.

If your age is continuous (rather than age brackets) then it would be a covariate. If your age is given as age-brackets, then it wont be covariate.