Ice cold water doesn't increase your metabolism, but it may use an extra 1 - 2 calories to bring it to body temperature. You decide if it's worth it.
There aren't any studies that show more fat is burned when we exercise on an empty stomach (not just in the morning). It's one of those gym "urban legends", along with the "fat-burning zone".
As for vitamins, a good multi-vitamin is recommended for those of us restricting calories because it can be hard to meet all our daily requirements. I'm not aware of any other vitamins that help with weight loss. As women, we need to monitor our calcium intake but that's not weight-related. And fish oil is highly recommended as a source of omega 3's, but again, it won't have an impact on weight. Just health.