Prove or disprove those languages are regular
For number 1, you're entirely correct. Every string in $\Sigma *$ is in this language. Take an arbitrary string of zeroes, ones, and twos, then let $y$ be that string, and $w$ be empty.

For number 2, the standard way I learned to prove it's not regular is with "fooling sets". The Pumping Lemma also works here.

For number 3, consider that there are only finitely many possibilities for $w$. This means you could, in theory, write a regular expression that just listed all of them. So this one is actually regular, through "brute force".