After I had prayed, I found a drop of menstrual blood and was unsure when that happened; what is the ruling on my prayer and fast?
All praise is due to Allah, peace and blessing be upon the Messenger of Allah.
Your prayer and fast are correct ,and you should not make up for them, and we ask Allah, The Almighty, to duely reward you for these acts of worship. Your menses start once you see blood because the situation remains as such unless there is certainty or predominant conjecture, as per the Fiqh maxim: "Certainty is not removed by doubt". And Allah Knows Best.
Are all the children of a suckling woman considered brothers to the strange child whom their mother had breastfed, or just to the one who had suckled with him?
All the children of the woman who had suckled a strange child are considered his/her brothers and sisters.
Are dream interpretation books accurate?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon Prophet Mohammad and upon all his family and companions.
Dream interpretation books are unreliable because they are merely expectations, not rulings of Sharia. However, if one sees a dream which one does not like, one should spit on one's left side and seek the refuge of Allah from the satan; it will not do one any harm, and one should not disclose it to anyone. If one sees a good vision, one should feel pleased but should not disclose it to anyone but whom one loves. And Allah The Almighty Knows Best.
Should vowed fast be offered in consecutive days, or not?
Vowed fast should be offered in line with what was originally intended by the vow-maker, either consecutively, or not.