] Sari--do you (or anyone else) know if everyone voted in such an election, or if was only people of the court, or people who could read, or some other criterion?

In Sweden The King was elected by landstings, a sort of precursors for local parliaments, where nobility, clergy, peasants and I think later even merchants of the province had representation. The nobility and hihger clergy of course had much more power in the matter than other estates. Kingship was relatively weak institution in medieval Scandinavia and King's most important role was to be the war leader (something Denmark seems to be needing in Hamlet).

When king Haakon gave a declaration for Finland to be allowed to be represented in the election, he specified that Finland should send 12 peaseants, an unspecified number of clergy and the highest crown official in the country to take part in the election (Finland did not have much in the way of nobility during the 14th century - nobody in their right mind would want to come here).

I suppose Shakespeare just took the idea of elective kingship from his sources and transplanted it in a court which resembles more a Tudor court than a real medieval system of government.