A cursed win will end in a draw by repetition against a perfect opponent. If the opponent is less than perfect, Stockfish might still win.
No, a cursed win is cursed. The WDL50+ tablebases assume that the 50-move counter was just reset, which is entirely realistic since they will normally be probed directly after a capture that brings the position into TB territory. (When the root position is already a TB position, you need DTZ information to see if a regular win can still be won within the remaining 50-move budget.)2) If an engine probes Syzygy right after capturing/pushing Pawn and see cursed winning/losing, can it consider them as sure winning/losing since 50-move-rule has just reset?
They are not correct3) If 1 & 2 are correct, can the engine continue searching Syzygy until capturing/pushing Pawns to make sure the probe result is sure winning or sure draw?
The WDL50+ probe done in the middle of the search returns the truth (assuming a perfect opponent). In case of a cursed win, there is no point in searching further in the hope of improving on the result returned by the probe, since the search also assumes a perfect opponent.