Pros/Cons of AP Ekko in general:

Pros:
- Massive Damage
- Outplay Potential with E
- Offers a Lockdown (W)
- Good Teamfighting Potential
- Mobility
- Assasin Potential
- Re-do Button


Cons:
-Hard Late Game
-Quite Squishy
-Extremly Hard Vs Peel Supports
-Vulnerable to CC
-Easy to mess up
-Poor to build tanky .

Clear with your Timewinder, Close the Gap with your Phase Dive or provide your Team with CC with your Parallel Convergence and unload massive AoE DMG with Chronobreak!
Assasination is much safer with Zed, Anivia deletes minions, Lissandra provides way more CC and Brand has much more AoE DMG.

Try using your Phase Dive to dodge important Abilities and push in the wave to roam.
Of course on some of these things lies your focus, for example if your laning vs a LeBlanc.

--- One important thing you have to do is the E+Q Combo very fast. A trick for this is to Phase Dive and while your in the E Animation, you press Timewinder to cancel the Q Animation. --

MUCH IMPORTANT :

Cool trick is the " Unseen W".
When you cast your W, a clone will appear. This is enough for the Enemie to know you've just placed a W on their head.
But if you hide behind a Wall or in a Bush, the clone is not visible for them.
When you pushed in the minion wave, hide in a bush or behind a wall and cast your Parallel Convergence. The Enemie will simply walk towards you to farm but then BAM! You Phase Dive, while the Parallel Convergence is right on top of them to stun them.
This lets you get a free passive proc plus a full Spell rotation on your Enemie, leaving them with roughly 2/5 HP on their Lane.

You would like to wait until the Enemies wasted their CC Spells, or Shields/Heals on their Carry
Look for opportunities to land a great W (Example "Initiator" Playstyle) or to catch the Carrys off guard.

Said this be careful when You play in the fight ! But also play Ekko with fun ! He is so cool like a champ.
So the guide it's just finish , I hope You like it and will be also useful for you.

See you in the game , maybe with Ekko. ( :D ) .