Nothing alike
Looks nothing like old Akali. Akali had a point-and-click Q , dash had no cost and could be used three times in a row, had stealth, and dealt hybrid damage.
This is no more like old Akali than the current Diana is. She's still a pure AP diver without any escape tools, and just has all-in potential in-lane. Hell she's more like an AP Talon than an Akali.
New Diana is basically old Diana with R as a common skill and W being reworked into a much stronger R.
When played correctly, the kit looks exactly the same as old Diana, except what made her dangerous is now no longer a an R.
Depends on how you look at it. But I don't think that will be the case since Diana's double dash will be here at level 2 instead of level 6.
Also, old Akali had single target damage whereas this diana will one shot an entire team with all her aoes. So the dashes make them look alike, but what's gonna happen when Diana jumps on their target will be totally different, given the fact that Diana is also a lot more tanky than a random assassin.