Oh, boy.
As owner of a Zone VI, I've recently asked most of those questions. The second plug is for a heating element (which I'm told has a thermostat); it's to keep the light at a reasonably constant temperature, since the light output of fluorescent tubes (like the one in a cold light) varies a lot with temperature. The 5-pin DIN connects to a CdS light metering cell that can be used with either a stabilizer or a compensating timer to get constant exposures even if the tube temperature varies over the course of a single exposure -- the stabilizer with keep the light output constant by varying input voltage, while the integrating timer will simply count "different length seconds", shorter when the tube is brighter and longer when it's dimmer.
The light doesn't get terribly hot -- I've left mine on for about fifteen minutes continuously, so far (haven't printed with it yet -- but will this weekend!) and it hardly gets warm to the touch, as would be the case with most fluorescent lighting fixtures. In my Omega enlarger, the Zone VI cold light sits down inside the original condenser housing, with the tubes and a diffusing sheet directly above the negative carrier. Your Vivitar probably doesn't have a large enough head to permit this if it's only 6x6 capable, and anything that mounts the light further from the negative will make for dimmer light and accompanying longer exposures.
For that matter, I note that my Zone VI, made for 4x5, is quite dim with a 35 mm negative in place, and the 50 mm printing lens stopped down to f/8, as it would be for exposure; much less than 10% of the diffuser area is illuminating the negative compared to the 4x5 format the head is designed to light. As a result, especially with split filtering using maximum cutoff filters, I expect I'll run into some longish exposure times with small negatives (my smallest format is Minolta 16, 10x14 mm image area), though that will be less and less of a problem as I go up through 6x4.5, 6x6, 6x9, and 9x12 cm.