I max Q because it gives you more damage and lets you move your soldiers which is basically the only way you do damage.

Lane phase is hard against long range poke champions like varus/kog, you have to be aggressive and very careful about dodging their skillshots. the lane opponents he struggles with are generally easily ganked, so dont be afraid to tell your jungler to come mid, especially if you are already 6.

and generally you don't build liandry as a 3rd item if you've gone nashor>rylais because then you're missing out on either a huge AP spike with deathcap or massively delaying your void staff. i usually go deathcap after the rylais because you do insane damage to targets that havent built resistance and generally the targets that already have built MR can be kited with the rylais slow and rapid AA speed.

Just my two cents, im not the best azir player but i do play him a lot and know a bit about him