What happens when you Magical Hack a Quicksilver Fountain?
Lands with flood counters on them retain their latest type even if Quicksilver Fountain is hacked or leaves the battlefield.
That is because the Fountain's first ability is not a static effect itself, but a triggered ability that creates a one-shot effect that in turn creates a continuous effect. Each flood counter has its individual effect at the time it's placed on a land. As an analogy, you can think of flood counters as token enchantments, except it's a counter instead.
That means your option 2) is correct. Lands that got a flood counter before the Fountain was hacked remain islands after the hack, flood counters after the hack turn lands into swamps, and all lands with flood counters retain their respective type after the Fountain has left the battlefield.


Continuous Effects

611.1. A continuous effect modifies characteristics of objects, modifies control of objects, or affects players or the rules of the game, for a fixed or indefinite period.
611.2. A continuous effect may be generated by the resolution of a spell or ability.