Reassignment isn't the same as mutation. But mutation depends on the type of value. If gender was a string like "female" it wouldn't be mutable cuz strings are immutable in JS.
var isn't global unless it's not inside a function. var is just function scoped, with declaration auto hoisted to the beginning of the function. let is a little more intuitive since you can't refer to it before it's been declared and has block scope rather than function scope.
Kind of. With hoisting, the compiler/interpreter will find variable declarations and execute them before executing the rest of the code. Hoisting leaves the variables as undefined until the code assigning the value to the variable is executed. Hoisting does not initialize the variables.
For example:
console.log(foo);
var foo;
//Expected output: console logs 'null'
console.log(foo === undefined);
var foo;
//Expected output: console logs 'true'
This means you can essentially write your code with variable declarations at the end, but it will still be executed as though the declarations were at the beginning. Your initializations and value assignments will still be executed as normal.
This is a feature that you should probably avoid because I honestly cannot think of any good use case for it that won't end up causing confusion, but it is important to understand that every variable within your scope will be declared at the beginning of execution regardless of where it is written within your code.