Does the NYC 2 Train Stop at Rector Street in Brooklyn?

No. The 2 train runs in Brooklyn to Flatbush Avenue–Brooklyn College. Rector Street is in Manhattan, served by the 4 and 5 trains (and the 1 train at nearby Rector St on the Broadway–Seventh Avenue Line). To reach Rector Street from Brooklyn, take the 2 to a transfer point (e.g., Borough Hall) and switch to the 4/5.