I know this may be a dumb question, but what are the screws on the humbucker for, and does screwing them do anything? I have adjusted pickup height, but never knew what these do, or if it is just a way of building humbuckers. (See Picture)

I could put something cliche here like "Music is Life", but I'd rather say.......Hello........Is it me you're looking for?!
Welcome to the forum.

They are for adjusting the output balance between the strings, like the staggered poles on many Fender-style single coils. For example, the screw pole of the first wound string is typically screwed out further than its adjacent plain string.

The effect of pole height on output is more noticeable if you play clean.
They adjust the volume of the string they are under. Closer to the string means louder. This is a gross gereralization. Also, they will come out at some point.
Do a search for "pickup height adjustment" and read the seymour duncan blog... best description I've seen. Their tip or using an accurate meter (like on a mixer or a laptop) to get a good balance is on the money. If you have a way to record on your computer, as they show in the blog, you'll be able to see and measure the exact difference. bear in mind, you'll never get them perfect, but using this method is much better than trying to do it by ear. Some people say to match the radius ("curve") of the neck, and while that's a starting point, in my experience that's usually way off.

I have one guitar where I'll never get the low E string quiet enough even with the pole (screw) all the way in. But using the recording method I was able to get everything as balanced as it can possibly be... much better than it was doing it by ear. BTW you can't really hurt your guitar by adjusting the poles, but be careful and read up a lot before you go turning things. Truss rods should be totally avoided unless you know what you're doing... pretty much everything else can be tweaked carefully if you've researched it so you at least have an idea of what you're doing.

I trust my ears when setting pole height, as I prefer the thickest plain string a bit quieter than the adjacent wound string, to take the hard edge off its sound. I agree that fretboard radius isn't a good indicator.

One oddity I have found is that my perception of optimum pole height can depend on the guitar. I have two guitars with the same pickups sets, SD Jazz, and very similar pots etc, but I cannot get the string-to-string balance as good in the 335 knockoff as I can in the bari, with the same relative tunings and strings. This pic shows the piece of steel I added to the slug poles to raise them a bit:

It did a good job of evening them out.