I want to take an image and (somehow) read it as an array of pixels. Meaning each element of the 2d array would be either a hex code or RGB 3-tuple that represent the color
What you are after is called color quantization. Several algorihtms have been designed, such as the Median Cut or the Popularity algorithm. They allow you to build an "optimal" color table with the desired number of entries.
These methods were popular in the times of expensive graphics cards, but have lost fame since the generalization of true color.
Complementarily to color quantization, one often uses color dithering, a method that restores some of the smoothness of color gradients and avoids banding effects.
https://nl.mathworks.com/help/images/reduce-the-number-of-colors-in-an-image.html?requestedDomain=true
Library (libraries) to use?
scikit-image or OpenCV would be my preferred choices.
Methods? (Are there any widely used algorithms for this kind of problem?)
K-means clustering is a popular approach to color quantization.
Am I using the wrong programming language? (Is there one that offers this kind of functionality but easier to use?)
Python is arguably the "easiest" language for this task.
DEMO
Consider this image:
The following code reduces the number of colors from +500K to only 6:
import numpy as np
from skimage import io
from sklearn.cluster import KMeans
original = io.imread('https://i.stack.imgur.com/QCl8D.jpg')
n_colors = 6
arr = original.reshape((-1, 3))
kmeans = KMeans(n_clusters=n_colors, random_state=42).fit(arr)
labels = kmeans.labels_
centers = kmeans.cluster_centers_
less_colors = centers[labels].reshape(original.shape).astype('uint8')
io.imshow(less_colors)
And this is how the color quantized image looks: