After that long discussion below, I won't go into much detail here. Actually, with what I answered below on the HCN = H2O problem, these should go well for you
(a) water is added --> dissolve
Fe(OH)2(s) + H2O ==> Fe^+2 + 2OH^-
So adding water moves the reaction to the left and the ppt dissolves.
(b) Fe(OH)2 is added--> neither
Adding more solid to a saturated solution can't make it dissolve more
(c) Solid Fe(NO3)2 is added--> precipitate
Addition of Fe(NO3)2 is adding Fe^+2 to the solution, that shifts the reaction to the left and causes more solid (ppt) to form.
(d) Solid KNO3 is added---> neither
KNO3 isn't involved in the reaction so it has no effect.