How much Fe++ could be present in water containing 1 x 1e-02 M HCO3-
(bicarbonate) without causing the precipitation of FeCO3 (Ksp=10**(-10.7))



What have you been taught about this. CO3^-2 must come from k2; therefore, I would write the ionization and k2 expression.

HCO3^- ==> H^+ + CO3^-2

k2 is of the order of 10^-11. I would plug in 1 x 10^-7 for (H^+) and solve for (CO3^-2).
Substitute (CO3^-2) in Ksp and solve for (Fe^+2)
Check my thinking.