Is the yellow discharge that appeared before menstruation and after its delay—given the presence of menstrual symptoms—considered a barrier to prayer and fasting, and is my period, which exceeds forty days, normal?

If you mean that your cycle is forty days or more, and the duration of the bleeding does not exceed fifteen days, then you are in menses as long as you see blood. When you become pure, perform ghusl and pray until your menstruation returns. There is no specific duration for the maximum period of purity between two menstrual cycles. As for yellowish discharge (ṣufrah), if it occurs during the customary period or is continuous with blood, then it is considered menses. Any yellowish discharge you see is not considered menses unless it occurs during your customary period or is accompanied by signs of menstruation. If the duration of the bleeding and any associated yellowish or brownish discharge (kudrah) exceeds fifteen days, then you are considered to have irregular bleeding (istiḥāḍah).