The Y block came out in 54, with the OHV 239. I know cause I own a 54 Customline with one in it
. The 53 was basically the same car, but with the Flathead.
As for the FE thing, over the years I've seen it argued back and forth, but coming from people who worked for Ford back then, it stood for Ford Edsel. I believe (but could be wrong), the FE made it's debut in the Edsel, hence the abbreviation.
As to what "size" motor it is, my opinion is that it is a big block. After all, it's one of the biggest motors Ford ever made (dimentionally). And it was always referred to as a big block, until the 385 series came out. Then the 385 series were known as big blocks, and the FE's started getting called FE's again.