Evaluate expressions without computing DTFT
For the first two questions you just need to use the definition of the DTFT
$$X(\omega)=\sum_{n=-\infty}^{\infty}x[n]e^{-jn\omega}\tag{1}$$
and use $\omega=0$ and $\omega=\pi$, respectively.
For 3. you just need to use the definition of the inverse DTFT:
$$x[n]=\frac{1}{2\pi}\int_{-\pi}^{\pi}X(\omega)e^{jn\omega}d\omega\tag{2}$$
Finally, for 4. and 5. you need Parseval's theorem. In addition, for 5. you need to express the sequence corresponding to the derivative of $X(\omega)$ in terms of $x[n]$. You should be able to either derive this yourself or look it up in a table.