Is there a literal syntax for mutable collections?

But, is there a literal syntax for creating an NSMutableArray or an NSMutableDictionary?

No. Best alternative:

[@[ @"foo", @"bar"] mutableCopy]

There isn't a built in way, but I just usually use mutableCopy like this:

NSMutableArray *array = [@[ @"1", @"2", @"3" ] mutableCopy];

Yes. But not quite. Take a look at this;

NSMutableArray *list = [@[] mutableCopy];

This creates a non-mutable array @[] and calls mutableCopy which returns a NSMutableArray *. In place of @[], you can give any array literal.

No. Just as how there isn't a syntax for creating an NSMutableString either. Mutable objects are not particularly suited to literal values.