'Freezing' Arrays in Javascript?

Yes, it is applicable to arrays too.

const arr = [1,2,3,4];
Object.freeze(arr);
Object.isFrozen(arr)// true
arr.push(5) // you will get a type error
arr.pop() // you will get a type error

Yes, freeze should work for Arrays, the behavior you are experiencing is clearly an implementation bug.

This bug might be related to the fact that array objects implement a custom [[DefineOwnProperty]] internal method (the magic that makes the length property work).

I just tested it on two implementations and it works properly (Chrome 16.0.888, and Firefox Aurora 8.02a).

About your second question, well, array objects inherit from Array.prototype which inherits from Object.prototype, for example, you can access non shadowed methods from Object.prototype directly on array objects:

['a'].hasOwnProperty('0'); // true

But this isn't related about how the typeof works, this operator will return 'object' for any object intance, regardless its kind, and for the null value, which people has always complained about.

The rest of possible return values of the typeof operator, correspond to the primitive types of the language, Number, String, Boolean, Symbol and Undefined.