Is it permissible for a woman to pray when mucus is coming out of her all day long? She tries to have a bath so that she will always be clean.
Yes, that is permissible, rather it is obligatory for her to offer the prayers on time, and that is not an impediment to her praying. You should understand that mucus and spittle do not invalidate wudoo’, and they are taahir (pure). The Prophet (peace and blessings of Allaah be upon him) allowed a worshipper to spit into his garment or under his foot whilst praying; this was narrated by al-Bukhaari, 500.