LD MAX When asymmetric with wings level and ball centred there is a balance between the asymmetric yawing moments from the live engine and the rudder side force; if you draw a picture you'll see that the resultant force (and therefore direction of flight) is not in line with the fuselage - hence sideslip with ball centred. A small amount of bank towards the live can give a sideslip to oppose the thrust-rudder resultant which can then achieve zero nett sideslip; in other words, minimum drag. I suspect (hope) your ME instructor covered this in the long brief for ME theory.
On your other point; turns in either direction are not an issue when asymmetric , this would have been demonstrated in asymm2. Min control speed is always an issue, regardless of whether straight or turning.
HFD