I think you're at least in part talking about the false consensus effect/bias
the false-consensus effect or false-consensus bias is an attributional type of cognitive bias whereby people tend to overestimate the extent to which their opinions, beliefs, preferences, values, and habits are normal and typical of those of others (i.e., that others also think the same way that they do). [...]
The false-consensus effect is not restricted to cases where people believe that their values are shared by the majority, but it still manifests as an overestimate of the extent of their belief. [...]
There is no single cause for this cognitive bias; the availability heuristic, self-serving bias, and naïve realism have been suggested as at least partial underlying factors.
At least your second example: "most people are X" being thought by someone who is X clearly belongs to this false-consensus-bias category.
I'm not sure your first example is quite like that though... being Italian is not something that can be reasonably assumed to be universal... but Wikipedia also mentions (2nd para quoted) that some seem apply the "false consensus bias" to describe even cases where the subjects just overestimates the extent of their belief.
The false consensus effect is thought to have some [cor]relation with the availability heuristic, or even be a causal effect of the latter... that seems to have been the ultimate conclusion of Larry's answer.
There's at least one paper starting with
Selective exposure to a biased sample of others is supposed to play an important role in explaining the false consensus effect (FCE).
And it also measured the level of correlation
Three predictions were tested. First, subjects were expected to refer to similar others more often than to dissimilar others. Second, referring to similar others was expected to lead to larger FCEs. Third, referring to dissimilar others was expected to lead to smaller FCEs. Results provided direct evidence of selective exposure, but this was most pronounced for issues for which opinions were relatively heterogeneous, i.e. for which there was no clear majority or minority opinion. The availability of similar others was further shown to be associated with larger FCEs, whereas the availability of dissimilar others was associated with smaller FCEs.
Other research suggest that there more moderators for the FCE:
Prior research has shown that individuals are often susceptible to a false consensus effect, whereby they overestimate the extent to which others share their opinions. In three studies, we show that the strength of the false consensus effect is moderated by the valence of one's own opinion, such that overestimation of population consensus is greater when an individual likes an alternative as compared to when she or he dislikes it. Further, we show that this moderation of false consensus is driven by the availability of countervalence attributes, that is, disliked attributes in liked alternatives and liked attributes in disliked alternatives.
So FCE seems more complex than being driven by mere availability, i.e. the level of like/dislike for the main characteristic as well as its associated/secondary characteristics seem to moderate FCE.
To speculate how this might influence your Italian example, subjects with a strong [and positive] ethnocentric perspective will probably exhibit more overestimation (of their percentage in the population). I don't know if anyone has tested this hypothesis though.
N.B. one study found that FCE persisted even after subjects were shown objective statistics. But the persistence of FCE is (thankfully and obviously) moderated by encountering disagreement.
Finally, one of those papers mentioned some synonyms for FCE that have been used in the literature: "assumed similarity" and "social projection".