$($Code as data$)$ Consider the following description of a three$-$tape TM $H.$

Also, define the following three TMs$,$ whose descriptions will be supplied as input to $H.$

Algorithm $3$: $M_2(x)$

Input : String xin$\{0,1{\}}^{**}$

$1.$ If $x=($:$M_1$:$),$ accept. Otherwise, reject.

$($a$)$ What is $L(M_1)?$

$($b$)$ What is $L(M_2)?$

$($c$)$ What is $L(M_3)?$

$($d$)$ Is $($:$M_1,M_2$:$)inL(H)?$ Explain why or why not.

$($e$)$ Is $($:$M_1,M_3$:$)inL(H)?$ Explain why or why not.

$($f$)$ What is the language $L(H)$ recognized by $H?$

$($g$)$ Is $H$ a decider for the language $L(H)?$ Explain why or why not.