If two events are independent, then $P(A|B)=P(A)$. If on the other hand, two independent drawings are made from two urns to determine whether you find at least one red ball, then the probability becomes $1-(1-(P(\not R_A))*(1-P(\not R_B))$ if $R_A$ corresponds to "drawing a red ball from urn A".
It is not straightforward to link this with yout sentence: "assuming the two attributes are independent in terms of success".
Given the numbers you have shown the first interpretation is not easy t apply as there are three "events": some one is over 35 (A), someone is male (B) and someone is successful (C).
Independen could mean: $P(C|A) = P(C|A \land B)$ and $P(C|B) = P(C|A \land B)$. But this only works if $P(C|A)=P(C|B)$, which is not the case in the example.
The second interpretation would be equivalent to saying: You basically have two indepndent shots at being successful, one is based on your age, one on yor gender (this makes of course not much sense conceptually or empirically, but would correspond to the run case). In this case I would calculate: $P(C)= $1-(1-(P(C|A))(1-P(C|B))=1-((1-0.25)(1-0.5))=1-0.375=0.625.
The answer by Hotaka uses yet another idea of independence that uses a sequential process: only for those candidates that are not successful based on the first criterion, is the chance for being successful based on the second criterion the specified probability. I would not consider this to be a valid case of independence.
Regarding the second question, I am a bit lost as to how binary attributes are linked to z-values here...