Can I move a unit, conquer, then use akali ability to move it back?

No — once the showdown closes and you Conquer, your unit is no longer "in a showdown," so Rogue Assassin's [Action] ability can't target it (it requires a friendly unit in a showdown).

You have to use Akali's ability during the Non-Combat Showdown, while you have Focus (Rule 347.1). But if you do that and your unit was the only one there, the showdown closes with no unit remaining — no Conquer, and the battlefield ends up uncontrolled. So retreat-and-Conquer with the same unit are mutually exclusive.

Two workarounds: keep at least one other friendly unit at that battlefield when you use Akali mid-showdown (the rest can still establish control and Conquer when the showdown closes), or just Conquer normally and Standard Move the unit back to Base afterward — but that exhausts it and doesn't use Akali. FAQ 11825; Rogue Assassin card text.