I see many women adding hair to their natural hair. Some of it human, animal and synthetic. Is it allowed? Secondly adding of false nails is it allowed?

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There is no problem in adding the (human and synthetic) hair if it is not covering the head scalp, which prevents water reaching the scalp for ablution or ghusl.
If it is, then it has to be removed for ablution and ghusl.
Also, it is not allowed if it taken from non-eatable animal, if you are going to pray with it.