your answer to 1 and 3 will depend largely on opposing team comp. Morello is a much more aggressive item than athene's bc it provides grievous wounds and more ability power than athene's. Whereas, athenes gives more less ability power, but also some magic resist. with azir, if the enemy team has a lot of ap, i would opt for athene's bc your top three items dont provide any mr. as for RoA or rylais, again depends on team comp. if you need tons of mr, go RoA. If you have opponents dealing %hp dmg or true dmg, Rylai's will give you more protection. for boots, lucidity all day. azir scales off CDR, so those are huge. your goal should be to hit 40% cdr. morello/athenes will get you 20%, lucidity another 15%. then you only need 5% from runes or masteries to get there.
edit: woops -- when I was talking about RoA, I was thinking of abyssal scepter. Abyssal scepter is a great option if you need additional MR. For RoA, it is a less aggressive option than Rylais bc Rylais has the slow and more AP. RoA will give you more health/mana, but less AP. As I said before, morellos is more aggressive than athenes. for a balanced approach, I think you will see a lot of athene/rylai combos or morello/RoA combos. But, I feel like the slow from Rylais gives more utility than grievous wounds. So you athene/rylai is probably the better option in most situations. if you really want to get aggro, go morello/rylai.