an hid can really help you control that temp during the winter and produce bud much better. just cycle your lights during the night and its also a heater. but also be prepared for it to get too hot inn your small grow area as well. personally, i prefer to veg under fluorescents because of the efficiency of the energy used.
you can introduce an hid. initially, keep a good distance between the bulb and the plant, then gradually mover her closer as she acclimates.
as far as how long it will be til harvest, it is really strain and environment dependent. generally, indoors, it should be between 8-14 weeks of flower. with your plant appearing to be indica dominant, there's a good chance she will be closer to 8.
here are the necessary nutrients for a cannabis plant: (macro) nitrogen, phosphorus, potassium, calcium, magnesium, sulfur, (micro) iron, boron, zinc, copper, manganese, molybdenum, chlorine, cobalt, nickel, and not sure if i missed any....
for fertilizer, there is more debate and myth than i could ever stay interested in. for a better recommendation, what have you been using so far?