Opponent has a random 2 might unit at random BF with a hidden card. I move in my random 4 might unit to that BF to contest. Opponent reveals switcharoo. That resolves. Chain is resolved and no other cards are played. Can i use akali legend to send my unit back to base? Combat doesnt start right?

Yes — you can. Combat does start here, but that doesn't block Akali: moving into a battlefield you don't control where an opponent has units applies Contested and opens the Showdown as the first step of Combat, i.e. a Combat Showdown (Rule 344.1).

A Combat Showdown is still a showdown, so Rogue Assassin's "[Action][>][T]: If it's your turn, move a friendly unit in a showdown to base" is legally timed while you hold Focus in Showdown Open. When Switcheroo resolves and the chain empties, Focus passes to you (Rule 346), so you do get the window before the Showdown closes.

Switcheroo swapping the Mights (your unit now 2) doesn't affect anything — only its Might changed, not its location or the fact it's in a Showdown. If you pull it, no combat damage is dealt, the opponent keeps control of the battlefield, and your unit sits at base (readied, if Akali is Empowered).