I Am Wanting To Lay Ceramic Tile On Top Of Wood Table. My Question Is, Can I Just Use A Tiling Putty Rather Than The Thinset/mortar, Then Grout The Table?

You can use premixed tile mastic to adhere the tile to the table, since you won't be walking on it.
  Thin-set mortar mix is generally used on floors. It provides a stronger bond, so it is important to use it when tiling floors because of the weight and heavy traffic.

You  can pick up  a (free) pamphlet on how to lay tile at the Home Depot store. It is a quick read and can usually be found in the tile department. If you don't see them, just ask an employee for one.
  You could also try practicing on a piece of plywood with liquid nail and tile mastic to see which method works the best for you.

My husband built a plant stand for me, the length of a coffee table about 4 ft high with a shelf.  
I have 4 squares of marble that I want to tile the top of the stand with.  Can I spread thinset ontop of the wood, lay the marble (once I break it up) and then grout?  I have been hearing a lot about backer board, what is that for?