The only option I see on bittrex is btc to zec. I do not show zec-btc therefore is it true I cannot trade zec-btc there?
that is one market, you don't show two different names just by swapping the place of the coin name and its base market to create a new one to sell and another one for buy orders. you buy and sell (aka trade) in same place. and it is better for programming too. when you see the word "something-another thing" something is the altcoin and the another thing is the base market. like ZEC-BTC, which means you buy ZEC with bitcoin as far as API calls are concerned.
