Take the example of a young star. It starts out as a huge cloud of gas, that is, for the most part, non rotating.
I read the rest, but I'm gonna cut you off right here.
Every cloud does have a small angular velocity, but because it's usually lightyears across, that comes out to a huge deal of angular momentum.
The mechanism for contracting clouds is not individual particle interactions, but gravity. The cloudcollapses under it's own weight. The same still applies with stars (and gas planets - Jupiter gives off twice as much energy as it recieves... guess where it comes from :thumbup

. The reason stars don't collapse, is because they're held back by another force, in this case radiation pressures. Same is not true for a nebula until it contracts so much, that it heats up and stars are born.
I meantioned that a nebula has a great deal of angular momentum... in fact, it has so much of it, that if only one star was born from it, it would have to spin so fast it would tare itself apart. The solution to the problem is that many stars are born and stars form their planets, which also take the angular momentum away (Jupiter has around 99% of angular momentum in our solar system).
Going back to your question, as I understand it: "Why does the stuff form a disk and not a rotating ball of gas?"
Well... this isn't a quick answer. There are many ways an accretion disk forms. Some of them form around dying stars... white dwarwes, neutron stars, black holes... the mechanism here is obvious: These stars didn't have a rotating ball of gas around them. The only answer is a disk.
"But what about accretion disks around proto stars, born inside of a gas cloud?"
I honestly don't know the answer to this one and will ask my professor, but if I had to speculate, it would come down to particle interactions. Collisions between particles would probably force the ball to collapse into a disk.
"So, why does the disk form with an inclination of 0°, relative to the star's rotation?"
My guess would be that the disk formed before the star, thus the star was bound to spin the same way...
It's an interesting question though and I'll ask my prof if there's a better explanation for that.