I cannot directly address the question relating to the Alhambra ticket because we didn't think to ask for the discount. However, during our trip last year the senior discount was available to anyone who could show proof of age which was my passport. And I think the age was 62. It worked in Seville, Cordoba, Madrid, etc. So I would assume it would work for the Alhambra. Also, for 5E you could buy a senior pass for the railroad that gave a 25% weekend and 40% weekday discount for the trains. Good for a year. We returned the following Fall and it worked like a charm.
I know in other countries, especially Italy where we have more experience, the senior discounts are restricted to EU citizens. I think the worse thing that could happen would be to make you pay an extra 3E. I would not buy another ticket.