There is a good list of airlines flying to and from Gran Canaria on this website:
http://www.grancanariainfo.co.uk/flights.aspHave a look at the low cost airlines - prices go up as you get closer to the date - so it's best to book as far ahead as possible.
I can't recommend any specific books, however the trails are generally well signposted - the walk around Roque Nublo is especially rewarding, though you will probably want some warm winter clothes to do that one in January.
There is a Parador (Spanish Government-run hotel) in the hills:
http://www.parador.es/en/tratarFichaPar ... 29&LANG=enThere are lots of reservoirs in the interior of the island and you will probably find lots of small streams at that time of year - I don't think that I'd risk drinking from them though.