Dough – How long and at what temperature and with what oil should doughnuts be fried

I just gave this recipe a try and the results were as follows:

1. The first doughnuts to be fried, sat in for the full time period listed in the recipe (3 minutes each side) and came out nearly black. The outside was severely overcooked while the inside seemed just about right.
2. Once the doughnuts rested until "warm" but not wet, they would not keep the toppings on them at all.
3. Keeping the oil temperature at the designated 350 degrees (F), was incredibly difficult. It fluctuated constantly between as high as 380 to as low as 340.
4. Leaving the doughnuts in for less than 3 minutes (2 minutes, then 1.5 minutes) produced slightly better color on the outside and the center remained fairly consistent. But the doughnuts still wouldn't take any toppings.
5. Moving the doughnuts directly from the oil to the toppings did get some of the toppings to stick to them but somehow the doughnuts cooled before they could be fully covered with the toppings.

I'm guessing that I did something wrong during the frying/timing of the doughnuts but the only substitution I made was to use sunflower oil instead of vegetable oil for the frying since I read somewhere else that sunflower oil was recommended.

What I'm looking for is consistency and ultimately the soft, tender texture of apple cider doughnuts with just the slight crunchy topping on the exterior. Of course, leaving all the doughnuts in for the same amount of time would get the same consistency but once I realized they were overdone, I decided to experiment to see if I could get it right by trying different things. No soap. So…

Does anyone know what the actual timing for doughnuts are while being fried? What temperature/time and with what oil should doughnuts be fried?

Thanks for your help!