Study in historical Slavonic grammar can help a lot. During university studies in Poland it is one year course. I don't know if there is or not such a handbook in English. But knowledge of historical development of language tells often whether it shall be ż or rz in some cases.
knowledge of russian surely helps in most instances
It would have to be all of the above, but let's pick on ś and sz.
sz is exactly like sh.. to pronounce ś.. start with the sh sound and then flatten your tongue and move the lower jaw slightly forward.. kind of like underbite a little.. teeth almost together and vertically lined up.
ę, ą, ź, ż, ć, dź etc are pronounced in a few various forms depending on their proximity to other sounds.
nope.. always the same
A native Polish speaker would easilly notice the error.
definitely.. ś and sz are not even close, really.