Are the yellow discharges and the brownish discharge that the questioner sees, which are connected to menstruation and never completely disappear, considered menses or istihada (bleeding outside of the regular menstrual period)? And what should she do if she does not have a known regular cycle, and is it permissible for her to wait eight days before performing ghusl (ritual bath)?

If menstruation begins in a way that makes it irregular, then you are experiencing استِحاضة (post-menstrual bleeding or irregular bleeding). If you do not have a regular cycle, then act based on differentiation: consider black blood as menstruation, and when it ceases, perform ghusl (definition) (ritual bath) and pray, and do not pay attention to yellowness. If you cannot differentiate, then observe a period of six or seven days of the month through diligent inquiry, and it is best to consider the condition of your female relatives (their typical cycle length). Anything beyond that is استِحاضة, and you should perform ablution for every prayer and pray, and you will have the rulings of ritually pure women.