Under the FIDE rules for quads, are the players ranked by rating and the last round colors randomized like under US Chess rules?
Also, does a FIDE rated tournament have to use FIDE Swiss or round robin pairing rules or can US Chess Swiss and round robin rules be used?
No. Positions are randomized. In the Berger tables, you can’t flip for last round colors (two players have already had repeated colors). The USCF quad tables alternate colors for the first two rounds so the third round pairs up the players who are due for the same color. If you did not randomize the original positions (i.e. you just filled in 1-2-3-4 in rating order), then there is no reason to give color advantage to any player based solely on rating order which is why the recommendation is to flip for color. If you did randomize (or more likely the computer randomized), then there is no reason to re-randomize in the last round, since everyone had the same chance of getting the W-B-W schedule.