Bbesides it's sole purpose of farming, Statik got nerfed to I dont think it's good anymore. And I'd prefer just full AP for better scaling into late game.

We go Shadowflame second item because of how strong you are once you get it. For example if you get it by 15 min, a lot of champs will only have a little over 1K HP by then. This means you get the full value of the item and can one-shot important targets. Since SF passive gives max pen when enemy is below 1k HP, meaning enemies will take the full 100AP from SF. And I also usually don't swap it for Void later since the enemy will get tankier late game.. Of course there are times you will go Hourglass second, like when you are losing lane, fighting one-shot Assassins like Zed, Talon, or Fizz, and if the enemy team has high kill pressure on you early.

Neither of the full items have the hextech alternator passive, so as long as you finish the first item before bulding the second hextech alternator I see no reasons why it can't work.

If played well, Akali should be fairly hard to kill, escape sticky situations, or turn fights. I usually would take Teleport if I'm trying to hard snowball the game, playing on the TOP lane, or if I'm up against a enemy laner that can roam really good like Talon, TF, and Ryze so I can help the side lanes. But I would recommend just using Flash if you are new to the champion. And Flash is also the more ideal summoner spell to bring.