[the heaven" (singular), despite the "shamayim", (plural)]
Anders,
Yes, while "shamayim" is a plural noun it describes a singular entity ala a "bunch" of grapes. Or another way of looking at it is that "in my fathers house (heaven) are many mansions (plural). This describes a singular place that is plural in nature. Also look up cherubim in your Hebrew dictionary and you will find a plural noun for the use of cherubim when in the text it is clear that only one cherubim is mentioned.
I leave translation from Hebrew to English to better people than I and spend my time learning proper English.
The three heavens mentioned in Genesis are Heaven (1:1), the firmament of heaven (1:6-8), and the open firmament of heaven (1:20). That John was called to the third heaven means that where he was is the "third heaven."