NSDictionary – Need to check whether dictionary contains key-value pair or not

Just ask it for the objectForKey:@"b". If it returns nil, no object is set at that key.

if ([xyz objectForKey:@"b"]) {
    NSLog(@"There's an object set for key @\"b\"!");
} else {
    NSLog(@"No object set for key @\"b\"");
}

Edit: As to your edited second question, it’s simply NSUInteger mCount = [xyz count];. Both of these answers are documented well and easily found in the NSDictionary class reference ([1] [2]).