Question

suppose I got a singleton class MySingleton as coded below.

Now is a singleton class just like any other class. I can have instance variables that are nonatomic and retain?

I can have: @property (nonatomic, retain) NSString* instanceVar in the .h file

and @synthesize instanceVar in the .m file?

static MySingleton* _sharedMySingleton = nil;

+(MySingleton*)sharedMySingleton
{
    @synchronized([MySingleton class])
    {
        if (!_sharedMySingleton)
            [[self alloc] init];

        return _sharedMySingleton;
    }

    return nil;
}

+(id)alloc
{
    @synchronized([MySingleton class])
    {
        NSAssert(_sharedMySingleton == nil, @"Attempted to allocate a second instance of a singleton.");
        _sharedMySingleton = [super alloc];
        return _sharedMySingleton;
    }

    return nil;
}

Answer 1

Yes, the instance of a singleton class behaves the same as a standard class, there is just one instance.

The pattern you have is overly complicated, there is no need for +(id)alloc
Here is a simplier pattern:

@implementation MySingleton
static MySingleton* _sharedMySingleton = nil;

+(MySingleton*)sharedMySingleton
{
    @synchronized([MySingleton class])
    {
        if (!_sharedMySingleton)
            _sharedSingleton = [[MySingleton alloc] init];
    }

    return _sharedMySingleton;
}