Q.Why Has My Nikau Palm Started To Die?
My Nikau Palm (native NZ palm) was doing alright during the last months after purchasing. Although, in the last days, it started to die. Its leaves went brown and smaller. It seems that it has some problem. Is it possible that I caused this by giving the palm too much water or what can be the issue?

Certified GKH Gardening Expert
It seems that you, already, have a good idea of what the problem is. The solution will come in the form of two things.
First, you will want to treat with a fungicide. This article will help:
https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm
Next will be proper watering. Watering should never be done on schedule. Watering should only be done once the soil dries, completely, down to about 2 inches. If there is any moisture, at all, down to this depth then you will want to hold off on watering. You can either check with your finger, or a moisture meter (which will be far more accurate).
Here is an article that will help you with fungicide use:
https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm
Since this species only occurs in NZ, there is not a whole lot of information available on the palm. In order to know what the perfect care routine will be, it will be necessary to know, exactly, what area it came from.
This article will give you a, general, idea of palm care, indoors:
https://www.gardeningknowhow.com/houseplants/palms/growing-palms-indoors.htm