A 1 Card game means that only one card will be drawn from the Source and placed into the Waste Pile at a time, while a 3 Card game means three are drawn and upturned in the Waste Pile at a time. There are no limits to how many times the Source deck can be cycled through in either style.
The stock pile contains cards that have not yet been moved to a foundation pile or tableau column. You can go through the stock pile as many times as you want turning over either 1 or 3 cards at a time depending on the setting of the Draw 3 option.