Given the following Joint PDF

\begin{equation\*}
f(x,y) = \left\{
 \begin{array}{ll}
 c & \quad -1< x \leq 1 ; \lvert x \rvert <y<1 \\
 0 & otherwise
 \end{array}
 \right.
\end{equation\*}
$1.$ Find the value of $c$.

$2.$ Find marginal PDF $f\_Y(y)$ of $y$

$3.$ Find conditional PDF of $X$ given $Y$

$4.$ Find covriance of $X$ and $Y$

$5.$ Are $X$ and $Y$ independent?

My attemept:

$part1$

I have found value of $c$ to be $c=1$

$Part2$

Marginal PDF of $Y$ is also found to be:
$ f\_Y(y) = \int\_{-1}^1(1)dx= 2$

$Part3$

The conditional PDF is also found to be $f(x|y)= f(x,y)/f\_Y(y)=1/2$

$Part4$

The covariance is given by:

$Cov(x,y)= E(XY)-E(X)E(Y)$

I don't know how to proceed further.

$Part5$

$X$ and $Y$ are independent when:

$P(X=x,Y=y)=P(X=x)P(Y=y)$ (Rest I don't know how to proceed further)

Please Help me in parts $4$ and $5$. How do I solve them