Correct.
> But why do we call it spin?
Because it is a physical quantity whose units are those of angular momentum, and we have to call it something.
> What are the possible values?
+/- h/4pi where h is Planck's constant. (It is usually written has h-bar/2 where h-bar is h/2pi.)
> Is it a magnitude or a vector?
It's a vector that always points in a direction corresponding to the orientation of the apparatus you use to measure it.
> Is there a reason we call it "spin" instead of "taste" or some other arbitrary name?
Yes. See above.
> How do you change it?
You can change an electron spin by measuring it along a different axis than the last time you measured it. The result you get will be one of two possible values. You can't control which one you get.
> What happens to it when particles interact?
Their spins become entangled.
So it can be written as a vector? No?
That's right. It's not a vector because it doesn't "transform" like a vector.
If you take a vector and rotate about an axis by 360 degrees, you get the same vector.
If you take a spinor and rotate it by 360 degrees you get a spinor which is "flipped". You have to rotate the spinor by 720 degrees to get back to the same spinor.
This is intrinsically weird, but that's QM.