It is not permissible for a menstruating woman to enter the mosque unless she is only passing through. However, she may sit in a place that is attached to the mosque or close to it and listen to the Khutbah.

A husband cannot have intercourse with his wife in the vagina when she is menstruating or in nifas. But he can be intimate by kissing, embracing, touching etc., parts that are above the navel and below the knee. Scholars differed on being intimate with regard to the area between the navel and the knee, apart from the front or back passage.

There is no need to do ghusl because of this discharge, and it does not affect the fast. With regard to prayer, wudu must be done for each prayer after the time for the prayer has begun, if the flow is continual.

Sex during periods is prohibited not just because of the blood, rather it is for many reasons as stated in the detailed answer below.

If the end of the period is ascertained by seeing the white discharge or complete dryness, then you should not pay any attention to the yellowish and brownish discharge in that case.