Is there NSMutableDictionary literal syntax to remove an element?

Yes, but... :-)

This is not supported by default, however the new syntax for setting dictionary elements uses the method setObject:forKeyedSubscript: rather than setObject:forKey:. So you can write a category which replaces the former and either sets or removes the element:

@implementation NSMutableDictionary (RemoveWithNil)

- (void) setObject:(id)obj forKeyedSubscript:(id<NSCopying>)key
{
   if (obj)
      [self setObject:obj forKey:key];
   else
      [self removeObjectForKey:key];
}

@end

Add that to your application and then:

dict[aKey] = nil;

will remove an element.

No. There is not. I have tried to find proof link but did not succeed :)

As of iOS 9 and macOS 10.11, these two are equivalent:

 [dictionary removeObjectForKey:@"key"];
 dictionary[@"key"] = nil;

See the Foundation release notes (search for the heading NSMutableDictionary subscript syntax change).