Q1. My gums bleed while fasting, do I have to re-keep the fast? 2. My nose bleeds sometimes due to heat, does my fast go through?
A1. You should try and spit the blood out, although the fast does not break with you swallowing it, (provided that the blood is less than the saliva when it is viewed.) It would be best to re-keep the fast later on. However, your current fast is still valid.
A2: As far as nose bleed is concerned, it would require you to make up for that fast.
Allah certainly knows best.