Problem designing a specific FIR filter
Think about how the output signal $y[n]$ is computed:

$$\begin{align}y[0]&amp;=x[0]h[0]\\
y[1]&amp;=x[1]h[0]+x[0]h[1]\\
y[2]&amp;=x[2]h[0]+x[1]h[1]+x[0]h[2]\\\vdots\end{align}$$

From the first equation above you know that the first coefficients of the FIR filter must equal $h[0]$. The second equation gives you $h[1]$ as the second coefficient, etc. So your intuition was correct: the FIR filter's impulse response is just a truncated version of the original impulse response.

For finding the difference equation, you don't need to compute any zeros or poles, you just need the coefficients:

$$y[n]=x[n]h[0]+x[n-1]h[1]+\ldots +x[n-1000]h[1000]=\sum_{k=0}^{1000}h[k]x[n-k]$$