Design a deterministic pushdown automaton for the language L$2=\{$w in $\{0,1\}$ : $|$#$0$w $$ #$1$w$|=<2\}.$

It is possible to construct this automaton using two states. True or False?

It may happen that $($in a correct solution$)$ on the stack a symbol corresponding to $0$ is placed on top of a symbol corresponding to $1.$True or false?

For the language L$3=\{$w in $\{0,1\}$ : $|$#$0$w$$#$1$w$|=<3\}$ we would need one more state in comparison to the number of states needed for L$2.$ True of false?

L$2$ is context$-$free. True of False?

Please answer