Simplyfing a particular boolean expression
I will use $\land$ instead of * and $\lor$ instead of +.

a) You could  simplify it as following: 

$ \ \ \ (y\land w) \lor y \lor w = (y\land w) \lor (y \land T) \lor w = y\land(w \lor T) \lor w = (y \land T) \lor w = y \lor w$

b) and prove it as following: 

Since $x \land y = x$ we have $\lnot x \lor \lnot y = \lnot x$ by De Morgan's law. By substituting $\lnot x$ in the given equality we have 
$$\lnot x \land \lnot y = (\lnot x \lor \lnot y) \land\lnot y = (\lnot x\land \lnot y) \lor (\lnot y \land \lnot y) = (\lnot x\land \lnot y) \lor \lnot y = $$
$$=(\lnot x \lor T)\land \lnot y = T \land \lnot y = \lnot y$$

Recall that for any boolean $x$ and $y$ the following identities always hold


$x \lor T = T$
$x \land T = x$
$x \land x = x$
$x \lor x = x$
$\lnot(x \land y) = \lnot x \lor \lnot y \text{ (De Morgan's law)}$
$\lnot(x \lor y) = \lnot x \land \lnot y \text{ (De Morgan's law)}$