Was there ever a design of an aircraft that incorporated armour covering the entire surface of the machine? I'm not talking about plates designed to protect the pilot/engine or other defensive measures increasing the chance of survival of the aircraft and it's operator. Just armour preventing penetration of the entire structure.
No. Such an aircraft would be too heavy to take off. Standard thickness of most aircraft skin is only 0.032" to 0.051" thick aluminum. Something like 0.125" might stop FlaK, but to do that everywhere would double the weight of the skin. To actually stop bullets, you'd need thicker steel skin...roughly 0.25-0.5" against armor piercing rounds, meaning the skin would be 15 to 30 times as heavy (steel being roughly 3x the weight of aluminum). Weight is everything in aircraft design. It affects all aspects of performance, from range to payload to maneuverability.
For example, the US attempted to up-armor and up-gun B-17s to escort bomber formations until longer-ranged escort fighters became available. The resulting YB-40 was 4,000lbs heavier (without bombs) than a fully loaded B-17F model. It could just barely keep up with the bombers heading to the target, and could easily fall behind on the return. That in addition to abysmal handling and poor fuel consumption (made worse by the additional drag from the second dorsal turret).