Hi Olbrat,
>Was it designed to be used against specific aircraft (other than whatever was in it's way)?
It was designed as a night fighter. It was a bit special in having a flexible top turret - this indicates a special doctrine of use that apparently did not have any actual operational application later.
Though it's often considered "the first purpose-built night fighter", it's worth noting that for all practical purposes, the Heinkel He 219 was a purpose-built night fighter too, though due to the multi-purpose doctrine of the Luftwaffe, other roles were considered (but never implemented). Originally, the He 219 designation had been used for a high-speed reconnaissance aircraft with a contra-rotating central propeller like the He 119, but the later He 219 night fighter actually has nothing in common with that design study except the designation.
>Was it easy/enjoyable to fly?
An important advantage of the Northrop P-61 over other contemporary designs was its very low single-engine safety speed. The rudders appear to have been exceptionally effective, allowing the pilot to use full power on one engine if the other one failed even at low speeds without loss of control. In combat operations at night where you might come home with battle damage, the ability to go around on one engine when something goes wrong on landing is a definite plus!
You can find a historic P-61 manual in this thread:
http://www.ww2aircraft.net/forum/other-mechanical-systems-tech/p-61-pilots-manual-6789.html
(The first publicized image of the then-secret P-61 was a drawing in one of Milton Caniff's comic strips, by the way. He had seen the prototype in flight, failing to appreciate that despite being flown in broad daylight over a major city, it was still supposed to be secret - reportedly, he got into a bit of trouble with the authorities for that strip!)
Have fun!
Henning (HoHun)