I don't think so. I suspect real sensory input are very different from imagined ones, it's just that most of these differences aren't preserved by the process that turns sensory inputs into memories.
Meh. To a conscious mind this makes no difference internally.
I sometimes have to experimentally verify whether a stimuli is real or imagined. Like moving closer to the perceived source of a sound/noise to see if it gets louder or not. If it does, it's real, if it doesn't, then it isn't. As far as I know, this isn't a particularly unique thing that happens only to me.
Another one for the memory-is-really-unreliable file. Some researchers at UC Irvine (one of them is Elizabeth Loftus, whose name I've seen attached to other fake-memory studies) asked about 5000 subjects about their recollection of four political events. One of the political events never actually happened. About half the subjects said they remembered the fake event. Subjects were more likely to pseudo-remember events congruent with their political preferences (e.g., Bush or Obama doing something embarrassing).
Link to papers.ssrn.com (paper is freely downloadable).
The subjects were recruited from the readership of Slate, which unsurprisingly means they aren't a very representative sample of the US population (never mind the rest of the world). In particular, about 5% identified as conservative and about 60% as progressive.
Each real event was remembered by 90-98% of subjects. Self-identified conservatives remembered the real events a little less well. Self-identified progressives were much more likely to "remember" a fake event in which G W Bush took a vacation in Texas while Hurricane Katrina was devastating New Orleans. Self-identified conservatives were somewhat more likely to "remember" a fake event in which Barack Obama shook the hand of Mahmoud Ahmedinejad.
About half of the subjects who "remembered" fake events were unable to identify the fake event correctly when they were told that one of the events in the study was fake.