No (not normally on factory systems; some after market systems allow that).
Can be either; better ones are color. If color, at night (dark) most switch to B/W.
Important feature: the viewing angle. The Toyota/Lexus ones (the only one I am familiar with) are EXCELLENT and allow an extremely wide viewing angle ( I'm guessing 150-170 degrees ), so much in fact, it's almost like you're looking "around the corner". Not quite, of course, but being mounted so far in the back, it really helps to see traffic beyond that "obese" SUV parked next to you as you pull out of your parking spot and as soon as your bumper clears the SUV, before you ever have a chance to see it from over your shoulder.
2011 Silver SL+QC [Mfg: 11/2010] 36mo/15k LEASE
06Jun2013 Status [28.5 months][34,173 miles][11 bars]
Lost CapacityBar 6/6/13 @34,173 miles while in LEAF Battery Monitor: 83.41%, 71.4F (avg); cool overnight;