I'm not aware of any turbo props with counter rotating props
A400?
The props on the prototype P-38 turned inwards at the top. The aircraft was written off after only 11:50 flying. Following wind tunnel tests outwards rotation at the top was found to be best, for the reason it gave the least pitch change from power on to power off, thus giving the pilot a more stable gun platform. The prototype rotation was the worst that could have been chosen, while rotation in the same direction lay between the worse and best. See graph below.
From the P-38 manual (abbreviated, but to give you a feel) Engine failure on take off - lift off is made at 100 mph, retract gear when certain you are airborne. Gear up the aircraft accelerates quickly to the single engine safety speed of 130 mph, the minimum airspeed at which the aircraft can be flown with gear up is 130 mph (gear contributes 60% of the total drag).
Failure with less than 130 mph cut both throttles and stop. Retract gear if necessary.
Failure with 130 mph or more and the gear up or starting up. Reduce power to gain directional control, then apply as much power as you can hold. While correcting jettison stores. Trim & feather. Excessive yaw will cause the vertical tail to stall and rudder forces will reverse. Engine power will need to be materially reduced and considerable rudder force applied to regain control. Situation can be prevented by keeping the aircraft flying straight by prompt rudder action and necessary throttling of live engine.
With one engine at normal rated power the aircraft can climb above 20,000 feet and have a TAS greater than 225 mph.