1) As you note, blood found in the toilet water is treated as a stain on a surface that is not mekabel tum’ah (susceptible to ritual impurity), since the toilet in which it is found is attached to the ground.

The timing of noticing the stain does not affect this halacha even though the sensation of urinating might mask a halachic sensation of menses (hargashah). Rather, the presumption is that in order to notice a stain in the water after urination, a woman would need to stand up or otherwise move, and the time it takes to do so would be considered sufficient delay after urination so that concerns of masked hargashah would not be relevant to evaluating it.

2) This rule does not change during the clean days.

3) Halachic consensus considers toilet water as a surface that is not mekabel tum’ah, on which stains may be disregarded. Ashkenazi halachic decisors are generally more concerned than Sefardi authorities regarding blood found immediately following urination, to which the usual leniencies of stains may not apply.

The position that a delay makes a difference in evaluating the relevance of masked hargashah is widely accepted, and is rooted in the Talmud, further developed in halachic codes, and articulated in particular with respect to cases like this by Rav Moshe Feinstein.

We hope that this answers your questions. Please let us know if we can be of further assistance.