No, the 3 lights on the front of the router are not normally lit. Only the tiny recessed light on the bottom of the router illuminates to indicate the power is on.
I haven't found any noticeable speed decrease using the ethernet adapter.
The Starlink wifi router continues to operate normally when using the etherner adapter. You may be thinking of when you put the Starlink router in bypass mode to use a third party wifi router. In that case the Starlink router wouldn't provide a wifi signal, but both the eternet adapter and the third part router should work normally.