Is it permissible to perform ablution by immersing the limbs in a vessel containing a very small amount of blood, and does the presence of some hairs in this vessel affect it?

It is not legislated to perform ablution by dipping one's limbs into a vessel containing a small amount of water, because that makes it musta'mal (used) water, and thus it is not sufficient [for purification], unless the water is abundant. As for blood, if it changes the water, ablution with it is not valid. Even if it does not change it, but it is a small amount and impure, the water becomes impure. The presence of hair in water does not affect its purity if the water is abundant or scarce and has not changed, especially if it is from a human or a ritually slaughtered animal. This is the view preferred by Sheikh al-Islam Ibn Taymiyyah.