How can I create an empty n*m PNG file in Python?

from PIL import Image
image = Image.new('RGB', (n, m))

You can use the method PIL.Image.new() to create the image. But the default color is in black. To make a totally white-background empty image, you can initialize it with the code:

from PIL import Image
img = Image.new("RGB", (800, 1280), (255, 255, 255))
img.save("image.png", "PNG")

It creates an image with the size 800x1280 with white background.

Which part are you confused by? You can create new images just by doing Image.new, as shown in the docs. Anyway, here's some code I wrote a long time ago to combine multiple images into one in PIL. It puts them all in a single row but you get the idea.

max_width = max(image.size[0] for image in images)
max_height = max(image.size[1] for image in images)

image_sheet = Image.new("RGBA", (max_width * len(images), max_height))

for (i, image) in enumerate(images):
    image_sheet.paste(image, (
        max_width * i + (max_width - image.size[0]) / 2,
        max_height * 0 + (max_height - image.size[1]) / 2
    ))

image_sheet.save("whatever.png")