Well, the problem is most likely the fact that it didn't fire. The cause of the problem - that's not so easily determined. It could be one or more things from a list of many things which can cause a firearm to malfunction.
NO
The .357 has a longer case and a heavier bullet; it is identical to a .38 in diameter but far more powerful. This is why a .38 will fire in a .357 but not the other way around.
10-100 USD or so
There are a dozen different cartridges with 38 in their name, and SOME are compatible with the .357 Magnum. A .357 will fire .38 Special, .38 Short Colt, .38 Long Colt- but NOT .38 S&W.
Yes. Your revolver will fire either one.
No, the only .357 auto is a Sig. Different shaped chamber.
No.
the 380 is a 9mm short
No.
Where can you buy .38 rimfire ammunition from
yes
Never heard of a PB 38