I usually run 3 ad reds (helps with last hitting), then the rest mp reds. All armor yellows (assassin mids coming in strong), half ap blues and half mr blues. and ap quints. This setup is pretty standard for being able to duel most mid laners and cs properly. Without resistences you will guarantee get murdered early levels because base damage is so much higher than base resistance early on. And the problem with Azir early game is once you move with your q, you don't have any ability to reposition your soldiers.
Maybe swap out your cdr in your runes because you're going to get it in your items. I feel its better to have base stats to help compensate your early level dueling weakness.
Ideally as Azir you want to get to a two item power spike. That might be nashors and morellos, nashors athenes, or (ideally) nashors rylais. Reason is Azir is super item reliant. His kit is good, but not great early levels.
You want to extend the laning phase as long as possible. Everytime i've played Azir with a cs lead i've won. Reason is he scales super hard, and synergies so well with all the items he uses. So early levels it's def a lot better to take smart trades and rack that cs up. If your opponent is a roamer you want to keep the pressure constantly on the lane.
The longer i've played Azir the more I learned to play conservative in the lane. Certain match ups you can be the clear cut bully, but theres other match ups where he falls short because of all ins.
*****So a trick i picked up from bjerg is, if you're in a lane where you can out poke them, what you want to do is clear the first three minions with autos, drop a solider on the back line, and if your opponent stays in solider range or near it, q it towards him. He will either be forced to drop back or go all in on you. You can out sustain lvl 2 all ins by kiting backwards. ****
Lastly, you should never lose hope when you play Azir. He brings so much to the table that all it takes is for you to get the items you need and you can be a force. Keep your spirits up when you're losing and just play smart. Hope this helps! Have fun :)
edit: your mana issues might stem from overly relying on abilities to farm. Be sure to be comfortable csing with autos. Also, it might help to take an early back to get a second dorans and some pots. Then tp back to lane. I've found that the early back for dorans really helps to speed up the building process.