WAR is only how you compare to the players at the same position. Xander has a .332 wOBA (weighted on-base average) which ranks 4th among all qualified SS in the league (Tulo is at .336 for comparison). He's 3rd among SS in base running, and he's a respectable 8th in defense. It's hard to find a SS nowadays who isn't taking something off the table either defensively or offensively, to have someone who is largely above-average at all facets of the game at a premium position = the 3.7 WAR.
correct. the defensive fielding spectrum has to be taken into account to truly assess a player's value. Basically, anyone who plays down the center of the field (CF, SS, 2B, P, C) has the most defensive responsibilities, so the amount of offensive production is commensurate to the inverse of these responsibilities.
general order is: DH > 1B > LF > RF > 3B > CF > 2B > SS > C > P (in order of increasing defensive responsibility, though obviously the pitcher is a special case where the defensive responsibility extends beyond fielding to actual pitching and pick offs).
It's what made A-Rod's early 2000s seasons so much more ridiculous than anything any non-Bonds player was doing at the time. Also why the debate between him and Ortiz for the 2005 MVP was ridiculous, A DH brings far less to the table than a replacement level fielding 3B with identical offensive stats. Gonna be a huge black mark on baseball if Shrek is ever inducted into the HOF before A-Rod.