The easiest way to understand this is to remember that when a pixel is transparent, its colour becomes irrelevant, yet it is retained.
So, if we make an opaque 512x512 image of random noise, like this:
convert -size 512x512 xc:gray +noise random a.png
and check its size, you can see it is 1.5MB:
-rw-r--r--@ 1 mark staff 1.5M 26 Oct 09:14 a.png
If I now make an otherwise identical, transparent version:
convert -size 512x512 xc:gray +noise random -alpha transparent b.png
You can see the file has got bigger (at 1.7MB), because it is now storing transparency AND the original random data. I won't show the image because there is nothing to see:
-rw-r--r--@ 1 mark staff 1.7M 26 Oct 09:16 b.png
I can now make the transparency layer fully opaque and the random pixels become visible again - so they were still there all along - even when the image was transparent:
convert b.png -alpha opaque c.png
If, however, I make the pixels transparent again, AND also set them all to the colour of the image background (since their colour is irrelevant), like this:
convert -size 512x512 xc:gray +noise random -alpha transparent -alpha background d.png
-rw-r--r--@ 1 mark staff 1.8K 26 Oct 09:22 d.png
And now suddenly the 1.5MB file is nearly 1,000 times smaller at 1.8K because it compresses much better as all the (invisible/transparent) colours are one single, solid background colour.
In answer to your question about coordinates. We can make a little image like this:
convert -size 1x1 \
xc:red xc:cyan +append \
\( xc:yellow xc:magenta +append \) -append a.png
And dump it like this:
convert a.png txt:
# ImageMagick pixel enumeration: 2,2,65535,srgb
0,0: (65535,0,0) #FF0000 red
1,0: (0,65535,65535) #00FFFF cyan
0,1: (65535,65535,0) #FFFF00 yellow
1,1: (65535,0,65535) #FF00FF magenta
And see that pixel coordinates in ImageMagick start at top-left corner.