I want to write a story about a girl who becomes incontinent through long term diaper usage
It doesn't. The muscles weaken, but even people that go 24/7 for years will tell you that if they want to hold it, they can. They can't do it for like 10 hours like someone that's used to it, but even after years of not holding it, they could still hold it a few hours if needed.
Does the bladder fill up as it would normally, and then just decide to empty when it wants?
Does the pee leak out all the time, resulting in a constantly wet pussy/diaper?
From what I've heard, it's more like your body just starts to subconsciously void when it notices it has to go. So neither. It's not a constant thing, but it's not like it fills up completely either. It's more like when you get the signal that tells you that you need to go, they will just react to that right away and wet. If they didn't want to wet though, they could consciously make an effort to hold it.
Would the person feel herself/himself releasing, or is the amount so small that they wouldn't?
They notice.
How often would a person have to be changed? Do people like leaving it past that point?
If left unchanged, what are the stages of discomfort? Does it get itchy and the skin rashy, or is it just too cold?
I've heard it's ideally at least 3 times a day, plus some time to "air out" to avoid getting diaper rash. Some people like leaving it past that point, but rashes are painful. It's essentially inflammation. You can google "diaper rash" to see what it looks like.
When masturbating, does the pee become just another lubricant or is it a turn off/kept separate?
This sounds like it depends on the person. I, personally, don't find it intrinsically a turn-on. I know some that do, and I know some that are grossed out by it and it's a turn-off. As for it being a lubricant, it's better than nothing, but it's about similar to water. It doesn't replace lube.
Does the pee come out with enough force to make a sound? Or does it just silently dribble out?
No sound, unless you really force it out. Even then it wouldn't be that loud.
Do long term diaper wearers sometimes poop out of convenience, like if the diaper needs to be changed soon anyway?
Again, that's up to the individual. I think the majority would say no. Even if they're about to change, messing is just a whole extra level of cleanup that's a huge pain. It changes a 5 minute change into possibly needing to take a shower.
Are there leakage issues with positioning and posture, etc.?
Of course. Most notably lying on your back can leak out the top if it gets too full, same with lying on your stomach. Lying on your side is usually the worst for leaks, though. They don't put padding on the sides.
do guys angle their penises upwards or downwards when wearing?
I do it down, I know others that do it up. It's a preference. I've found it seems to be partly related to how sexual it is. Most of the people I know that point up are turned on by diapers. If they point down, it bends awkwardly for them.
Does it make any difference regarding leakage?
Definitely. Guys that point up have leaking problems out the top of the diaper fairly often. When you point up, it winds up being pretty close to the edge, especially if it's because you're hard.
You're saying you want to know this to write stories, but I think that having so many stories that are unrealistic shows that people don't strive for realism in their fap fiction. People are turned on by being forced into diapers and becoming incontinent within a week, even though that's practically impossible short of surgery. They also often like being refused changes for hours, or even days, even though that would be awful IRL. Try less "how does this work" and more "what do people want".
TL;DR: You read too much diaper fap fiction.