Yes, calcium sulfate is roughly twice as soluble as calcium hydroxide. Actually the question contains a glaring mistake, which I will come to later.
Let's talk about the addition of calcium nitrate. In a situation of competing equilibria, between precipitation of the hydroxide or precipitation the sulfate, hydroxide precipitates first, and hydroxide will continue to precipitate until almost all the calcium ions have been removed, and only if an excess of calcium nitrate is added will the sulfate begin to precipitate. In real life, this means you won't get a clean separation.
Now that mistake I mentioned; what happened to the added nitrate ions? Of course they end up in Filtrate 2, so actually none of the options is correct.