Yes an empty string is falsy, however new String("") is not.

Note also that it's well possible that

if (x) { ... }

is verified, but that

if (x == false) { ... }

is verified too (this happens for example with an empty array [] or with new String("")).

Yes. All false, 0, empty strings '' and "", NaN, undefined, and null are always evaluated as false; everything else is true.

And in your example, b is false after evaluation. (I think you mistakenly wrote true)

The set of "truthy" and "falsey" values in JavaScript comes from the ToBoolean abstract operation defined in the ECMAScript spec, which is used when coercing a value to a boolean:

+--------------------------------------------------------------------------+
| Argument Type | Result                                                   |
|---------------+----------------------------------------------------------|
| Undefined     | false                                                    |
|---------------+----------------------------------------------------------|
| Null          | false                                                    |
|---------------+----------------------------------------------------------|
| Boolean       | The result equals the input argument (no conversion).    |
|---------------+----------------------------------------------------------|
| Number        | The result is false if the argument is +0, −0, or NaN;   |
|               | otherwise the result is true.                            |
|---------------+----------------------------------------------------------|
| String        | The result is false if the argument is the empty String  |
|               | (its length is zero); otherwise the result is true.      |
|---------------+----------------------------------------------------------|
| Object        | true                                                     |
+--------------------------------------------------------------------------+

From this table, we can see that null and undefined are both coerced to false in a boolean context. However, your fields.length === 0 does not map generally onto a false value. If fields.length is a string, then it will be treated as false (because a zero-length string is false), but if it is an object (including an array) it will coerce to true.

If fields should be a string, then !fields is a sufficient predicate. If fields is an array, your best check might be:

if (!fields || fields.length === 0)

For checking if a variable is falsey or if it has length attribute equal to zero (which for a string, means it is empty), I use:

function isEmpty(str) {
    return (!str || str.length === 0 );
}

(Note that strings aren't the only variables with a length attribute, arrays have them as well, for example.)

Alternativaly, you can use the (not so) newly optional chaining and arrow functions to simplify:

const isEmpty = (str) => (!str?.length);

It will check the length, returning undefined in case of a nullish value, without throwing an error. In the case of an empty value, zero is falsy and the result is still valid.

For checking if a variable is falsey or if the string only contains whitespace or is empty, I use:

function isBlank(str) {
    return (!str || /^\s*$/.test(str));
}

If you want, you can monkey-patch the String prototype like this:

String.prototype.isEmpty = function() {
    // This doesn't work the same way as the isEmpty function used 
    // in the first example, it will return true for strings containing only whitespace
    return (this.length === 0 || !this.trim());
};
console.log("example".isEmpty());

Note that monkey-patching built-in types are controversial, as it can break code that depends on the existing structure of built-in types, for whatever reason.