Answered by Shaykh Faraz Rabbani
1) What is the minimum amount of blood that would invalidate one’s ablution if it is present on one’s clothes? What about other types of filth (like urine, or water used to clean off filth)?
Blood does not affect one’s wudu if merely present on one’s clothes.
However, it is a condition for the validity of the prayer that one’s body, clothing, and places of where one’s limb touch the ground in prostration be free of filth beyond the excused amount. [Ala’ al-Din Abidin, Gifts of Guidance]
The extent of one’s inner palm (about 5 cm in diameter) or less of filth is excused, though recommended to remove. More than this amount prevents the validity of one’s prayer. [ibid.]
2)Does bleeding invalidate fasting? If so, is there any minimum amount of blood that is forgiven? What if the person bleeds often due to cracks in the skin in cold dry weather?
Bleeding does not affect the validity of one’s fast.
3) Does the presence of oil or cream on the skin nullify ablution if the ablution is done after applying the oil and/or cream on the skin or hair? If yes, is there any condition ( like forming a layer over the skin)?
No, unless it is so thickly applied that it forms a clear, perceptible barrier between the water and the skin, which would be rare (and would require ingenious folly).
And Allah alone gives success.