FIR Filter Magnitude Response

This is the shape of the bipolar amplitude function for a FIR filter with odd m:

I have 2 questions :

1. 
   

   If i want to use this FIR as a low pass filter between 0 and $\frac{F_{c}}{2}$ , how can i set the value of $G(f)$ to 0 between $\frac{F_{c}}{2}$ and $F_{c}$ ?

   
   


2. 
   

   My prof said that i can use the this FIR as a lowpass between 0 and $\frac{F_{c}}{2}$, but if i want to use the filter between $\frac{F_{c}}{2}$ and $F_{c}$ does it still behave as a lowpass ? (what does it mean that in that range $G(f)$ takes negative values ? )