This particular しく is not the 連用形【れんようけい】 of adjective ending し (modern しい). Instead, this is past recollective auxiliary き in the 連体形【れんたいけい】 + the ク語法【ごほう】, a.k.a. "-ku nominalization" pattern similar to uses of modern こと, seen in Old Japanese and persisting in certain set expressions even into modern usage, such as 曰【いわ】く ("history;...
Yes, that な is the irrealis form (未然形) of ぬ from classical Japanese. ぬ is usually the auxiliary for the perfective aspect (as in 風立ちぬ), but when it's combined with an auxiliary of inference such as ん (=む), it emphatically adds the degree of certainty.