Does bleeding from the nose invalidate the fast? Does touching a non-mahram woman invalidate the fast? What is the ruling on using perfumes and Vicks while fasting?

Blood that exits a fasting person involuntarily does not break the fast, whether it is little or much. This is because there is no text that mandates breaking the fast due to it, nor does analogical reasoning (qiyas) require it, similar to wounds and nosebleeds.