1)Is it possible in mid November to just turn up or is it best to book in advance.?
Its possible indeed!..just check out even at the high end range as well and just bagain..you can even find a luxuary room for GBP 18.
The other side of it is that you must have that special patience to go look around peacefully and find that dream hotel after a long journey. You will be greeted everywhere with "YOU WANT ROOM SIRS??" from autodrivers, hoteliers..and you name it.
2)Rough cost for a taxi from trivandrum airport to varkala.
At the airport, there is a pre-paid taxi service counter provided by the airport authorities. They will charge you INR 1200.