Is there a time of the year where there is always a sunset in Norway?

Answer 1

No.
As in all countries the sun goes up and down.
The difference with places farther south is that the difference between length of day (and night,) is much greater.
So in summer the days are very long, (in the north even round the clock,) and in winter the day is very short, it does not even get really light in the middle of the day.
But the rest of the day is like the rest of the world, light in the summer days.
And dark in the winter nights.
And in spring and fall the days are like the rest of the world.

Answer 2

The summer is when the sun doesn't set in the extreme north.