Yes the stole over the Gospel thing is something I encountered for the first time at the Romanian mission here in Seattle two years ago.
This is pretty much a universal pious practice, as far as I can tell. I've seen it in EP parishes, in Greece, in Romania, in Bulgaria, in Ukraine. However, it seems to be the most common in the Romanian tradition, especially during the Gospel readings during the Euchelion
In every Greek parish I've attended (which is 3 of them), after Vespers everybody went home. Why is that?
Because no one wanted to go to confession.
Also, do most of the EP priests pray the Great Litany or any of the other Confession prayers to prepare for hearing the confession?
Most? Who can say? There are a variety of prayers, including the trisagion, a litany, psalms, etc., in every ieratikon
. Most EP priests to whom I have confessed have followed what's in their particular copy.