Let the language L be defined as:

L$=\{$ww$"$re$"|$wE $\{0,1)",2\{0,1)"]$

where:

$$w is the reverse string of w$.$ For example, if w $=100,$ then wR $=001.$

$$I is the reverse string of X$.$ For example, if x $=110,$ then xR $=011.$

$10,1)$ represents the set of all binary strings, including the empty string.

Please answer the following three questions:

$$Is the language regular or not?

$$Is the language context$-$free or not?

$$If context$-$free, please construct a pushdown automaton $($PDA$)$ that recognizes the language.