Teleport is good for Zilean. This summoner spell will allow you to engage and stay in lane, but this summoner spell can be change into other spells is needed, such as barrier, cleanse, or ignite.

When buying items, try building Rod of Ages first buy buying either Catalyst of Aeons or Blasting Wand(I recommend Catalyst) and next buy Tear of the Goddess. This will allow you to play more spells and later burst damage. If the KDA is about 5 kills to 0 death or 3 kills to 1 death, Mejai's Soulstealer might be a good item to build. After finishing Archangel's Staff, and maybe Sorcerer's Shoes, Void Staff might be necessary for extra damage and penetrate any Magic Resist, because you burst a lot of damage with Rod of Ages and Archangel's Staff. Later buy Rabandon's Deathcaps to increase the damage. Zhonya's Hourglass and Guardian Angel are good for staying in battle, and Seraph's Embrace will appear after max stacks from Archangel's Staff.

I recommend upgrading "Q" first then "W" so you can deal more damage and land more stuns. "E" is your getaway/engage and "R" will help you and your team last longer.

Yasuo is a melee type champ that needs enemy creeps to dash. Bullying with "auto" and stun on enemy/ally creep help against Yas. "Kat's like Yasuo, but a bit harder. Landing you stun might be easier, but she can counterattack. To prevent Kat from roaming, harass her with 'auto' and slow her down for some stuns." -Old Man Roshi. Ahri pokes a lot, but drain mana. If you can land at least 1 "Q" on her, then your good against her. his shadows, its hard to land "Q" on him, and he deals too much damage as an assassin, counter to Zilean. Same thing with LeBlanc. She will dash to you and bust you down pretty fast.