Calculating ppm of an ion in a solution
You are wrong. Assuming that you are doing ppm in terms of mass: There are $0.0055$ grams of $\ce{Fe(NO3)2}$. Its molar mass is $179.8548$ grams/mol. Thus, you have $3.058022\!\times\! 10^{-5}$ moles. Multiplying this by the molar mass of iron gives you $0.00170775$ grams of $\ce{Fe}$. Thus, you have $0.0037922$ grams of $\ce{NO3}$. The concentration of iron is 
$$\mathrm c = \ce{\frac{Fe}{Water+Fe(NO3)2}} = \frac{0.00170775}{0.0055+2000}= 8.538726518 \times10^{-7}$$
Thus, $\ce{Fe}$ has a $\pu{ppm}$ of $0.85$