How can spectrum of DTFT of sampled band-limited analog signal be in $[-\pi,\pi]$
The DTFT $X_d(\omega)$ of a discrete-time signal is periodic with period $2\pi$, so it's sufficient to consider the interval $[-\pi,\pi]$. "Restricted" to this interval means that due to the inherent periodicity there can be no new frequency components outside the interval $[-\pi,\pi]$. Of course, $\pi$ corresponds to half the sampling frequency.

If $X_a(\Omega)$ is the spectrum of a band-limited continuous-time signal, and if the sampling frequency is greater than twice the band-width, then the equality

$$X_d(\omega)=\frac{1}{T}X_a\left(\frac{\omega}{T}\right)$$

holds in the interval $[-\pi,\pi]$. Outside that interval, $X_a(\Omega)$ is zero, and $X_d(\omega)$ is continued periodically.