Dette er sant for meg. Hunden min jager faktisk ekorn i snøen. Og noen ganger fanger hun dem.
does this word come directly from the german for to hunt, or do they both share a germanic ancestor?
It has its root in the Proto-Germanic word "*jagōną", but entered the Norwegian language via Middle Low German.
Yes, though the less common "ekorner" does exist for the plural.
I'd avoid the masculine declination pattern, unless you enjoy getting odd looks from Norwegians.