What is the ruling on blood that appeared six days after intercourse and six days after the end of menstruation, and it consisted of simple spots and lasted for six days, and what is the ruling on prayer during these days, knowing that the blood was dark red?

The blood that appeared six days after your period is not menses, because the minimum period of purity between two menstrual cycles is fifteen days. This blood is irregular bleeding (istihadah), and it permits the performance of acts of worship and conjugal relations, provided that your usual menstrual days have concluded and you have verified its cessation by observing the white discharge (al-qassah al-bayda') or dryness.