"Δεξιά "κι" αριστερά" is the right
What is the difference between δεξιά and Δεξιά?
It's the same between right and Right. A capitalised first letter.
Would the greeks naturally say it in this order? In (british) english it sounds more natural to say 'left and right'.
I'd say we favour δεξιά - αριστερά to αριστερά - δεξιά. I think context may have something to do with it though, as has dropping κι or not.