Can you store fish in the Selling tank with out them being sold? Will the fish only be sold if you are in the sell screen?

Yes, any fish you have in the selling tank will stay there unless you go to the selling screen (selecting the "Sell Fish" button). In the selling screen, people will buy any adult fish in the selling tank.

If you raise the price much higher than they are worth, they won't be bought in that screen. However, you may then get stuck with fish you like in the isolation tank and no way to sell the fish in your selling tank...

So just be careful!