Discard a card to gain money
No, thats incorrect, you can not chose to avoid taking a card from the structure and discarding a card from your board for money.

The rules state under Game Turn :-


  "On your turn, you must choose an “accessible” card in
  the card structure and play it. An accessible card is a card which
  isn’t partially covered by other cards."


Note it says the structure, not anything in your play area.  'Structure' being the term for how cards are laid out each age. You then have a choice with the card you selected to build it, discard it for money, or construct a wonder.

So to answer your question, the only card you may discard for money is the one you took from the structure that turn and no other.  You do not pay any costs associated with building a card if you are just taking it to discard for money.